Does removing a creature from the battlefield during the blockers declaration phase affect the damage the player will take? [duplicate]

Question

First example: When a creature is going to attack me alone and I use Vapor Snag to return it to the other player's hand, is the combat damage prevented?

Second example: If three 1/1 Soldier creatures are going to attack me while Veteran Swordsmith (which gives other Soldier Creatures +1/+0) is on the board and I use Doom Blade to kill the Veteran Swordsmith, do I take 3 damage or 6?

Third example: I control a creature, but couldn't use it to block a sliver my opponent controls because he just put a Shifting Sliver into play. If I use Path to Exile to exile his Shifting Sliver during the blockers declaration phase, does this make me able to block the other sliver?

Also, would this kind of play work in response to triggered/activated abilities? (for example, trying to prevent a triggered/activated ability from resolving by removing the permanent from the battlefield in response to the opponent trying to trigger/activate it)

Answer 1

Here's a breakdown of the five stages in the relevant part of the turn:

• Declare attackers step
  • (1) attackers are declared
  • (2) players get priority (to cast instants and activate abilities)
• Declare blockers step
  • (3) blockers are declared
  • (4) players get priority
• Combat damage step
  • (5) damage is assigned and dealt
  • ...

For the most part, you only check what something does and if it's legal right when it happens. So damage (dealt in stage 5) is only dealt by creatures that are still in combat at stage 5, and is based on their power at the moment stage 5 happens. Blocking (done in stage 3) is legal if it is legal at the moment stage 3 happens. So to answer your questions:

1) yes, since the creature is not still in combat at stage 5.

2) 3, since their power is 1 each by the time stage 5 happens.

3) As long as you use Path to Exile in stage 2 (or earlier in the turn), blocking the sliver will be legal since nothing will be preventing that when stage 3 happens. If you cast it during the declare blockers step (i.e. during stage 4) then it will be irrelevant because all blockers are declared in stage 3.