Theorem rexlimdvw 2672

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 2667	1 |- ( ph -> ( E. x e. A ps -> ch ) )

This proof depends on syntax axioms:   -> wi 4   e. wcel 2209   E.wrex 2529

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-ial 1587  ax-i5r 1588

This proof depends on definitions:  df-bi 117  df-nf 1514  df-ral 2533  df-rex 2534

This theorem is used by:  nnpredcl  4770  qsss  6868  fodjuomnilemdc  7484  ltpopr  7962  ltsopr  7963  ltexprlemlol  7969  ltexprlemupu  7971  cauappcvgprlemrnd  8017  caucvgprlemrnd  8040  caucvgprprlemrnd  8068  suplocexprlemss  8082  suplocexprlemrl  8084  suplocsrlempr  8174  climuni  12059  ellspsn  14754  cncnp2m  15332  bj-findis  17005