Theorem exlimdvv 1944

Description: Deduction from Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 31-Jul-1995.)

Hypothesis

Ref	Expression
exlimdvv.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
exlimdvv	|- ( ph -> ( E. x E. y ps -> ch ) )

Distinct variable groups:   ch, x   ph, x   ch, y   ph, y

Allowed substitution hints:   ps( x, y)

Proof of Theorem exlimdvv

Step	Hyp	Ref	Expression
1		exlimdvv.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	exlimdv 1865	. 2 |- ( ph -> ( E. y ps -> ch ) )
3	2	exlimdv 1865	1 |- ( ph -> ( E. x E. y ps -> ch ) )

Syntax hints:   -> wi 4   E.wex 1538

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-5 1493  ax-gen 1495  ax-ie2 1540  ax-17 1572

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  euotd  4341  funopg  5352  funopsn  5817  th3qlem1  6784  fundmen  6959  sbthlemi10  7133  addnq0mo  7634  mulnq0mo  7635  genprndl  7708  genprndu  7709  genpdisj  7710  mullocpr  7758  addsrmo  7930  mulsrmo  7931  cnm  8019  summodc  11894  fsum2dlemstep  11945  prodmodc  12089  fprod2dlemstep  12133  txbasval  14941