Theorem 2eximdv 1928

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 1926	. 2 |- ( ph -> ( E. y ps -> E. y ch ) )
3	2	eximdv 1926	1 |- ( ph -> ( E. x E. y ps -> E. x E. y 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-ia2 107  ax-ia3 108  ax-5 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-17 1572  ax-ial 1580

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  cgsex2g  2836  cgsex4g  2837  spc2egv  2893  spc3egv  2895  relop  4871  elres  5040  opabbrex  6047  th3q  6785  en2prde  7362  addnnnq0  7632  mulnnnq0  7633  prmuloc  7749  addsrpr  7928  mulsrpr  7929  upgrex  15897  umgredg  15937