Metamath Proof Explorer

Theorem bnj1538

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

Ref Expression
Hypothesis bnj1538.1 
|- A = { x e. B | ph }
Assertion bnj1538 
|- ( x e. A -> ph )

Proof

Step Hyp Ref Expression
1 bnj1538.1 
 |-  A = { x e. B | ph }
2 1 rabeq2i 
 |-  ( x e. A <-> ( x e. B /\ ph ) )
3 2 simprbi 
 |-  ( x e. A -> ph )