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  4345  opabssxpd  4760  funopg  5358  funopsn  5825  th3qlem1  6801  fundmen  6976  sbthlemi10  7156  addnq0mo  7657  mulnq0mo  7658  genprndl  7731  genprndu  7732  genpdisj  7733  mullocpr  7781  addsrmo  7953  mulsrmo  7954  cnm  8042  summodc  11934  fsum2dlemstep  11985  prodmodc  12129  fprod2dlemstep  12173  txbasval  14981