Theorem 19.26-2 1799

Description: Theorem 19.26 1798 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 1798	. . 3 |- ( A. y ( ph /\ ps ) <-> ( A. y ph /\ A. y ps ) )
2	1	albii 1747	. 2 |- ( A. x A. y ( ph /\ ps ) <-> A. x ( A. y ph /\ A. y ps ) )
3		19.26 1798	. 2 |- ( A. x ( A. y ph /\ A. y ps ) <-> ( A. x A. y ph /\ A. x A. y ps ) )
4	2, 3	bitri 264	1 |- ( A. x A. y ( ph /\ ps ) <-> ( A. x A. y ph /\ A. x A. y ps ) )

Syntax hints:   <-> wb 196   /\ wa 384   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  2mo2  2550  opelopabt  4987  fun11  5963  dford4  37596  undmrnresiss  37910