Theorem eximd 1503

Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

Ref	Expression
eximd.1	|- F/ x ph
eximd.2	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
eximd	|- ( ph -> ( E. x ps -> E. x ch ) )

Proof of Theorem eximd

Step	Hyp	Ref	Expression
1		eximd.1	. . 3 |- F/ x ph
2	1	nfri 1412	. 2 |- ( ph -> A. x ph )
3		eximd.2	. 2 |- ( ph -> ( ps -> ch ) )
4	2, 3	eximdh 1502	1 |- ( ph -> ( E. x ps -> E. x ch ) )

Syntax hints:   -> wi 4   F/wnf 1349   E.wex 1381

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-ial 1427

This theorem depends on definitions:  df-bi 110  df-nf 1350

This theorem is referenced by:  19.41  1576  mo2icl  2720  copsexg  3981  ssopab2  4012  eunex  4285