Theorem rexlimdvw 2618

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 2613	1 |- ( ph -> ( E. x e. A ps -> ch ) )

Syntax hints:   -> wi 4   e. wcel 2167   E.wrex 2476

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-17 1540  ax-ial 1548  ax-i5r 1549

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-ral 2480  df-rex 2481

This theorem is referenced by:  nnpredcl  4659  qsss  6653  fodjuomnilemdc  7210  ltpopr  7662  ltsopr  7663  ltexprlemlol  7669  ltexprlemupu  7671  cauappcvgprlemrnd  7717  caucvgprlemrnd  7740  caucvgprprlemrnd  7768  suplocexprlemss  7782  suplocexprlemrl  7784  suplocsrlempr  7874  climuni  11458  ellspsn  13973  cncnp2m  14467  bj-findis  15625