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  4872  elres  5041  opabbrex  6054  th3q  6795  en2prde  7377  addnnnq0  7647  mulnnnq0  7648  prmuloc  7764  addsrpr  7943  mulsrpr  7944  upgrex  15918  umgredg  15958