Theorem 19.26-2 1458

Description: Theorem 19.26 of [Margaris] p. 90 with two quantifiers. (Contributed by NM, 3-Feb-2005.)

Assertion

Ref	Expression
19.26-2	|- ( A. x A. y ( ph /\ ps ) <-> ( A. x A. y ph /\ A. x A. y ps ) )

Proof of Theorem 19.26-2

Step	Hyp	Ref	Expression
1		19.26 1457	. . 3 |- ( A. y ( ph /\ ps ) <-> ( A. y ph /\ A. y ps ) )
2	1	albii 1446	. 2 |- ( A. x A. y ( ph /\ ps ) <-> A. x ( A. y ph /\ A. y ps ) )
3		19.26 1457	. 2 |- ( A. x ( A. y ph /\ A. y ps ) <-> ( A. x A. y ph /\ A. x A. y ps ) )
4	2, 3	bitri 183	1 |- ( A. x A. y ( ph /\ ps ) <-> ( A. x A. y ph /\ A. x A. y ps ) )

Syntax hints:   /\ wa 103   <-> wb 104   A.wal 1329

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 1423  ax-gen 1425

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  opelopabt  4179  fun11  5185