Theorem exlimdvv 1869

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 1791	. 2 |- ( ph -> ( E. y ps -> ch ) )
3	2	exlimdv 1791	1 |- ( ph -> ( E. x E. y ps -> ch ) )

Syntax hints:   -> wi 4   E.wex 1468

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-5 1423  ax-gen 1425  ax-ie2 1470  ax-17 1506

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  euotd  4171  funopg  5152  th3qlem1  6524  fundmen  6693  sbthlemi10  6847  addnq0mo  7248  mulnq0mo  7249  genprndl  7322  genprndu  7323  genpdisj  7324  mullocpr  7372  addsrmo  7544  mulsrmo  7545  cnm  7633  summodc  11145  fsum2dlemstep  11196  txbasval  12425