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Metamath Proof Explorer

Theorem 19.28v

Description: Version of 19.28 with a disjoint variable condition, requiring fewer axioms. (Contributed by NM, 25-Mar-2004)

Ref Expression
Assertion 19.28v 
|- ( A. x ( ph /\ ps ) <-> ( ph /\ A. x ps ) )

Proof

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