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  4340  funopg  5351  funopsn  5816  th3qlem1  6782  fundmen  6957  sbthlemi10  7129  addnq0mo  7630  mulnq0mo  7631  genprndl  7704  genprndu  7705  genpdisj  7706  mullocpr  7754  addsrmo  7926  mulsrmo  7927  cnm  8015  summodc  11889  fsum2dlemstep  11940  prodmodc  12084  fprod2dlemstep  12128  txbasval  14935