Theorem reximdv 2462

Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Restricted quantifier version with strong hypothesis.) (Contributed by NM, 24-Jun-1998.)

Hypothesis

Ref	Expression
reximdv.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
reximdv	|- ( ph -> ( E. x e. A ps -> E. x e. A ch ) )

Distinct variable group:   ph, x

Allowed substitution hints:   ps( x)   ch( x)   A( x)

Proof of Theorem reximdv

Step	Hyp	Ref	Expression
1		reximdv.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	a1d 22	. 2 |- ( ph -> ( x e. A -> ( ps -> ch ) ) )
3	2	reximdvai 2461	1 |- ( ph -> ( E. x e. A ps -> E. x e. A ch ) )

Syntax hints:   -> wi 4   e. wcel 1433   E.wrex 2349

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-17 1459  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-ral 2353  df-rex 2354

This theorem is referenced by:  r19.12  2466  reusv3  4210  rexxfrd  4213  iunpw  4229  fvelima  5246  carden2bex  6458  prnmaddl  6680  prarloclem5  6690  prarloc2  6694  genprndl  6711  genprndu  6712  ltpopr  6785  recexprlemm  6814  recexprlemopl  6815  recexprlemopu  6817  recexprlem1ssl  6823  recexprlem1ssu  6824  cauappcvgprlemupu  6839  caucvgprlemupu  6862  caucvgprprlemupu  6890  caucvgsrlemoffres  6976  resqrexlemgt0  9906  subcn2  10150  bezoutlembz  10393