Theorem rexlimdvw 2551

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 2546	1 |- ( ph -> ( E. x e. A ps -> ch ) )

Syntax hints:   -> wi 4   e. wcel 1480   E.wrex 2415

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-i5r 1515

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-ral 2419  df-rex 2420

This theorem is referenced by:  nnpredcl  4531  qsss  6481  fodjuomnilemdc  7009  ltpopr  7396  ltsopr  7397  ltexprlemlol  7403  ltexprlemupu  7405  cauappcvgprlemrnd  7451  caucvgprlemrnd  7474  caucvgprprlemrnd  7502  suplocexprlemss  7516  suplocexprlemrl  7518  suplocsrlempr  7608  climuni  11055  cncnp2m  12389  bj-findis  13166