Theorem 19.23vv 1903

Description: Theorem 19.23v 1902 extended to two variables. (Contributed by NM, 10-Aug-2004.)

Assertion

Ref	Expression
19.23vv	|- ( A. x A. y ( ph -> ps ) <-> ( E. x E. y ph -> ps ) )

Distinct variable groups:   ps, x   ps, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem 19.23vv

Step	Hyp	Ref	Expression
1		19.23v 1902	. . 3 |- ( A. y ( ph -> ps ) <-> ( E. y ph -> ps ) )
2	1	albii 1747	. 2 |- ( A. x A. y ( ph -> ps ) <-> A. x ( E. y ph -> ps ) )
3		19.23v 1902	. 2 |- ( A. x ( E. y ph -> ps ) <-> ( E. x E. y ph -> ps ) )
4	2, 3	bitri 264	1 |- ( A. x A. y ( ph -> ps ) <-> ( E. x E. y ph -> ps ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by:  ssrel  5207  ssrelOLD  5208  ssrelrel  5220  raliunxp  5261  bnj1052  31043  bnj1030  31055