Crumbling Santuary/Corrupt

[waffles]

What happens if crumbling santuary is in play and i cast Corrupt? I know the santuary removes the cards, but do i gain the life?

Crumbling Sanctuary
 

Artifact

For each 1 damage that would be dealt to a player, that player exiles the top card of his or her library instead.
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Corrupt

 

Sorcery
Corrupt deals damage equal to the number of Swamps you control to target creature or player. You gain life equal to the damage dealt this way.

[silvernail]

No life gain, Sanctuary is a replacement effect.

[Godder]

To explain further, Corrupt says to gain life equal to the damage dealt, but the replacement effect means that the damage dealt is 0, so the life gain is also 0.