Theorem eximd 1548

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 1457	. 2 |- ( ph -> A. x ph )
3		eximd.2	. 2 |- ( ph -> ( ps -> ch ) )
4	2, 3	eximdh 1547	1 |- ( ph -> ( E. x ps -> E. x ch ) )

Syntax hints:   -> wi 4   F/wnf 1394   E.wex 1426

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-ial 1472

This theorem depends on definitions:  df-bi 115  df-nf 1395

This theorem is referenced by:  19.41  1621  mo2icl  2794  copsexg  4069  ssopab2  4100  eunex  4375  spc2ed  5990