Metamath Proof Explorer

Theorem bnj1230

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Hypothesis bnj1230.1 
|- B = { x e. A | ph }
Assertion bnj1230 
|- ( y e. B -> A. x y e. B )

Proof

Step Hyp Ref Expression
1 bnj1230.1 
 |-  B = { x e. A | ph }
2 nfrab1 
 |-  F/_ x { x e. A | ph }
3 1 2 nfcxfr 
 |-  F/_ x B
4 3 nfcrii 
 |-  ( y e. B -> A. x y e. B )