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Metamath Proof Explorer

Theorem r19.21

Description: Restricted quantifier version of 19.21 . (Contributed by Scott Fenton, 30-Mar-2011)

Ref Expression
Hypothesis r19.21.1 
|- F/ x ph
Assertion r19.21 
|- ( A. x e. A ( ph -> ps ) <-> ( ph -> A. x e. A ps ) )

Proof

Step Hyp Ref Expression
1 r19.21.1 
 |-  F/ x ph
2 r19.21t 
 |-  ( F/ x ph -> ( A. x e. A ( ph -> ps ) <-> ( ph -> A. x e. A ps ) ) )
3 1 2 ax-mp 
 |-  ( A. x e. A ( ph -> ps ) <-> ( ph -> A. x e. A ps ) )