Theorem reximdvai 2419

Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 14-Nov-2002.)

Hypothesis

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

Assertion

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

Distinct variable group:   ph, x

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

Proof of Theorem reximdvai

Step	Hyp	Ref	Expression
1		nfv 1421	. 2 |- F/ x ph
2		reximdvai.1	. 2 |- ( ph -> ( x e. A -> ( ps -> ch ) ) )
3	1, 2	reximdai 2417	1 |- ( ph -> ( E. x e. A ps -> E. x e. A ch ) )

Syntax hints:   -> wi 4   e. wcel 1393   E.wrex 2307

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 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-ral 2311  df-rex 2312

This theorem is referenced by:  reximdv  2420  reximdva  2421  reuind  2744