Theorem 2eximdv 1905

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 1903	. 2 |- ( ph -> ( E. y ps -> E. y ch ) )
3	2	eximdv 1903	1 |- ( ph -> ( E. x E. y ps -> E. x E. y ch ) )

Syntax hints:   -> wi 4   E.wex 1515

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 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-17 1549  ax-ial 1557

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  cgsex2g  2808  cgsex4g  2809  spc2egv  2863  spc3egv  2865  relop  4828  elres  4995  opabbrex  5989  th3q  6727  addnnnq0  7562  mulnnnq0  7563  prmuloc  7679  addsrpr  7858  mulsrpr  7859