Theorem exlimdvv 1820

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 1742	. 2 |- ( ph -> ( E. y ps -> ch ) )
3	2	exlimdv 1742	1 |- ( ph -> ( E. x E. y ps -> ch ) )

Syntax hints:   -> wi 4   E.wex 1422

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-5 1377  ax-gen 1379  ax-ie2 1424  ax-17 1460

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  euotd  4037  funopg  4984  th3qlem1  6295  fundmen  6374  addnq0mo  6751  mulnq0mo  6752  genprndl  6825  genprndu  6826  genpdisj  6827  mullocpr  6875  addsrmo  7034  mulsrmo  7035