Theorem rexlimdvw 2436

Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 18-Jun-2014.)

Hypothesis

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

Assertion

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

Distinct variable groups:   ph, x   ch, x

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

Proof of Theorem rexlimdvw

Step	Hyp	Ref	Expression
1		rexlimdvw.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	a1d 22	. 2 |- ( ph -> ( x e. A -> ( ps -> ch ) ) )
3	2	rexlimdv 2432	1 |- ( ph -> ( E. x e. A ps -> ch ) )

Syntax hints:   -> wi 4   e. wcel 1393   E.wrex 2307

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-i5r 1428

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-ral 2311  df-rex 2312

This theorem is referenced by:  qsss  6165  ltpopr  6693  ltsopr  6694  ltexprlemlol  6700  ltexprlemupu  6702  cauappcvgprlemrnd  6748  caucvgprlemrnd  6771  caucvgprprlemrnd  6799  climuni  9814  bj-findis  10104