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Metamath Proof Explorer

Theorem 19.27

Description: Theorem 19.27 of Margaris p. 90. See 19.27v for a version requiring fewer axioms. (Contributed by NM, 21-Jun-1993)

Ref Expression
Hypothesis 19.27.1 
|- F/ x ps
Assertion 19.27 
|- ( A. x ( ph /\ ps ) <-> ( A. x ph /\ ps ) )

Proof

Step Hyp Ref Expression
1 19.27.1 
 |-  F/ x ps
2 19.26 
 |-  ( A. x ( ph /\ ps ) <-> ( A. x ph /\ A. x ps ) )
3 1 19.3 
 |-  ( A. x ps <-> ps )
4 3 anbi2i 
 |-  ( ( A. x ph /\ A. x ps ) <-> ( A. x ph /\ ps ) )
5 2 4 bitri 
 |-  ( A. x ( ph /\ ps ) <-> ( A. x ph /\ ps ) )