Theorem 2eximdv 1817

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 1815	. 2 |- ( ph -> ( E. y ps -> E. y ch ) )
3	2	eximdv 1815	1 |- ( ph -> ( E. x E. y ps -> E. x E. y ch ) )

Syntax hints:   -> wi 4   E.wex 1433

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1388  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-4 1452  ax-17 1471  ax-ial 1479

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  cgsex2g  2669  cgsex4g  2670  spc2egv  2722  spc3egv  2724  relop  4617  elres  4781  opabbrex  5731  th3q  6437  addnnnq0  7105  mulnnnq0  7106  prmuloc  7222  addsrpr  7388  mulsrpr  7389