Theorem 2eximdv 1855

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 1853	. 2 |- ( ph -> ( E. y ps -> E. y ch ) )
3	2	eximdv 1853	1 |- ( ph -> ( E. x E. y ps -> E. x E. y ch ) )

Syntax hints:   -> wi 4   E.wex 1469

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-17 1507  ax-ial 1515

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  cgsex2g  2725  cgsex4g  2726  spc2egv  2779  spc3egv  2781  relop  4697  elres  4863  opabbrex  5823  th3q  6542  addnnnq0  7281  mulnnnq0  7282  prmuloc  7398  addsrpr  7577  mulsrpr  7578