Theorem 2eximdv 1904

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 1902	. 2 |- ( ph -> ( E. y ps -> E. y ch ) )
3	2	eximdv 1902	1 |- ( ph -> ( E. x E. y ps -> E. x E. y ch ) )

Syntax hints:   -> wi 4   E.wex 1514

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 1469  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-4 1532  ax-17 1548  ax-ial 1556

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  cgsex2g  2807  cgsex4g  2808  spc2egv  2862  spc3egv  2864  relop  4827  elres  4994  opabbrex  5988  th3q  6726  addnnnq0  7561  mulnnnq0  7562  prmuloc  7678  addsrpr  7857  mulsrpr  7858