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Metamath Proof Explorer

Theorem 19.27v

Description: Version of 19.27 with a disjoint variable condition, requiring fewer axioms. (Contributed by NM, 3-Jun-2004)

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

Proof

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