Theorem rexlimdvw 2430

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 2426	1 |- (ph -> (E.x e. A ps -> ch))

Syntax hints:   -> wi 4   e. wcel 1390  E.wrex 2301

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 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-i5r 1425

This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305  df-rex 2306

This theorem is referenced by:  qsss  6101  ltpopr  6569  ltsopr  6570  ltexprlemlol  6576  ltexprlemupu  6578  cauappcvgprlemrnd  6622  caucvgprlemrnd  6644  bj-findis  9439