Theorem 2eximdv 1935

Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 3-Aug-1995.)

Hypothesis

Ref	Expression
2alimdv.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
2eximdv	|- ( ph -> ( E. x E. y ps -> E. x E. y ch ) )

Distinct variable groups:   ph, x   ph, y

Allowed substitution hints:   ps( x, y)   ch( x, y)

Proof of Theorem 2eximdv

Step	Hyp	Ref	Expression
1		2alimdv.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	eximdv 1933	. 2 |- ( ph -> ( E. y ps -> E. y ch ) )
3	2	eximdv 1933	1 |- ( ph -> ( E. x E. y ps -> E. x E. y ch ) )

This proof depends on syntax axioms:   -> wi 4   E.wex 1545

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-ial 1587

This proof depends on definitions:  df-bi 117

This theorem is used by:  cgsex2g  2858  cgsex4g  2859  spc2egv  2915  spc3egv  2917  relop  4930  elres  5099  opabbrex  6132  th3q  6914  en2prde  7539  addnnnq0  7816  mulnnnq0  7817  prmuloc  7933  addsrpr  8112  mulsrpr  8113  upgrex  16344  umgredg  16386