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  5819  th3qlem1  6792  fundmen  6967  sbthlemi10  7144  addnq0mo  7645  mulnq0mo  7646  genprndl  7719  genprndu  7720  genpdisj  7721  mullocpr  7769  addsrmo  7941  mulsrmo  7942  cnm  8030  summodc  11909  fsum2dlemstep  11960  prodmodc  12104  fprod2dlemstep  12148  txbasval  14956