Theorem 19.28v 1893

Description: Theorem 19.28 of [Margaris] p. 90. (Contributed by NM, 25-Mar-2004.)

Assertion

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

Distinct variable group:   ph, x

Allowed substitution hint:   ps( x)

Proof of Theorem 19.28v

Step	Hyp	Ref	Expression
1		ax-17 1519	. 2 |- ( ph -> A. x ph )
2	1	19.28h 1555	1 |- ( A. x ( ph /\ ps ) <-> ( ph /\ A. x ps ) )

Syntax hints:   /\ wa 103   <-> wb 104   A.wal 1346

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 1440  ax-gen 1442  ax-4 1503  ax-17 1519

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  reu6  2919  dfer2  6514