Theorem exlimdvv 1826

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 1748	. 2 |- ( ph -> ( E. y ps -> ch ) )
3	2	exlimdv 1748	1 |- ( ph -> ( E. x E. y ps -> ch ) )

Syntax hints:   -> wi 4   E.wex 1427

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-5 1382  ax-gen 1384  ax-ie2 1429  ax-17 1465

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  euotd  4090  funopg  5061  th3qlem1  6408  fundmen  6577  sbthlemi10  6729  addnq0mo  7067  mulnq0mo  7068  genprndl  7141  genprndu  7142  genpdisj  7143  mullocpr  7191  addsrmo  7350  mulsrmo  7351  isummo  10834  fsum2dlemstep  10889