Theorem rexlimdv 2488

Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 14-Nov-2002.) (Proof shortened by Eric Schmidt, 22-Dec-2006.)

Hypothesis

Ref	Expression
rexlimdv.1	|- ( ph -> ( x e. A -> ( ps -> ch ) ) )

Assertion

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

Distinct variable groups:   ph, x   ch, x

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

Proof of Theorem rexlimdv

Step	Hyp	Ref	Expression
1		nfv 1466	. 2 |- F/ x ph
2		nfv 1466	. 2 |- F/ x ch
3		rexlimdv.1	. 2 |- ( ph -> ( x e. A -> ( ps -> ch ) ) )
4	1, 2, 3	rexlimd 2486	1 |- ( ph -> ( E. x e. A ps -> ch ) )

Syntax hints:   -> wi 4   e. wcel 1438   E.wrex 2360

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-17 1464  ax-ial 1472  ax-i5r 1473

This theorem depends on definitions:  df-bi 115  df-nf 1395  df-ral 2364  df-rex 2365

This theorem is referenced by:  rexlimdva  2489  rexlimdv3a  2491  rexlimdvw  2492  rexlimdvv  2495  trintssmOLD  3953  ssorduni  4304  funcnvuni  5083  dffo3  5446  smoiun  6066  tfrlem9  6084  ordiso2  6728  axprecex  7415  recexap  8122  zdiv  8834  btwnz  8865  lbzbi  9101