Theorem 19.27v 1887

Description: Theorem 19.27 of [Margaris] p. 90. (Contributed by NM, 3-Jun-2004.)

Assertion

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

Distinct variable group:   ps, x

Allowed substitution hint:   ph( x)

Proof of Theorem 19.27v

Step	Hyp	Ref	Expression
1		ax-17 1514	. 2 |- ( ps -> A. x ps )
2	1	19.27h 1548	1 |- ( A. x ( ph /\ ps ) <-> ( A. x ph /\ ps ) )

Syntax hints:   /\ wa 103   <-> wb 104   A.wal 1341

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-4 1498  ax-17 1514

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)