Theorem 2eximdv 1870

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 1868	. 2 |- ( ph -> ( E. y ps -> E. y ch ) )
3	2	eximdv 1868	1 |- ( ph -> ( E. x E. y ps -> E. x E. y ch ) )

Syntax hints:   -> wi 4   E.wex 1480

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 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-17 1514  ax-ial 1522

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  cgsex2g  2762  cgsex4g  2763  spc2egv  2816  spc3egv  2818  relop  4754  elres  4920  opabbrex  5886  th3q  6606  addnnnq0  7390  mulnnnq0  7391  prmuloc  7507  addsrpr  7686  mulsrpr  7687