Courageous Resolve doesn't prevent damage. Rather, it changes the results of that damage. For example, if a creature with lifelink deals damage to you, you won't lose any life, but its controller will still gain that much life. Similarly, if a creature with infect deals damage to you, you'll still receive that many poison counters.
Spells and abilities that would normally cause you to lose life still resolve, but the life-loss part simply has no effect.
Protection from your opponents means that the target creature has protection from each object controlled by those opponents. If an object has no controller (such as a card in a graveyard), its owner is considered its controller for this purpose.
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In a Commander game, combat damage you're dealt by a commander is still tracked, even if you don't lose life as a result.
Courageous Resolve checks your life total only at the time it resolves. If it's 5 or less at that time, even if you gain life later in the turn, you'll still be unable to lose life or lose the game that turn, and your opponents will still be unable to win the game that turn.
If you cast Courageous Resolve in a Two-Headed Giant game and your team's life total is 5 or less when it resolves, your team can't lose the game that turn and the opposing team can't win the game that turn.
Effects that replace an event with having you lose life (such as Tainted Remedy) will end up replacing the event with nothing.
Other circumstances can still cause you to lose the game. For example, you will lose a game if you concede or if you're penalized with a Game Loss or a Match Loss during a sanctioned tournament due to a tournament rules infraction.
You can't pay a cost that includes the payment of any amount of life other than 0 life. However, you can choose to be dealt damage, even though that damage won't result in your life total changing.
If an effect would cause you to exchange life totals with another player whose life total is lower than yours, the exchange won't happen. Neither player's life total changes.
If an effect says to set your life total to a certain number and that number is less than your current life total, that part of the effect won't do anything.
If you cast Courageous Resolve and your life total is 5 or less when it resolves, for the rest of that turn, no game effect can cause you to lose the game or cause any opponent to win the game. It doesn't matter whether you have 0 or less life, you're forced to draw a card while your library is empty, you have ten or more poison counters, you're at the end of your Nine Lives, your opponent is a Triskaidekaphile, and so on. You keep playing.
You can choose not to target a creature just to draw a card and, if you have 5 or less life, to get the additional effects listed. However, if you do choose a target, and that target is illegal at the time Courageous Resolve tries to resolve, it won't resolve and none of its effects will happen. You won't draw a card, and the additional effects won't occur even if you have 5 or less life.
Abilities that trigger whenever damage is dealt to you will still trigger because that damage is still dealt, even though your life total won't change as a result.
