Theorem exlimi 1605

Description: Inference from Theorem 19.23 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

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

Assertion

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

Proof of Theorem exlimi

Step	Hyp	Ref	Expression
1		exlimi.1	. . 3 |- F/ x ps
2	1	nfri 1530	. 2 |- ( ps -> A. x ps )
3		exlimi.2	. 2 |- ( ph -> ps )
4	2, 3	exlimih 1604	1 |- ( E. x ph -> ps )

Syntax hints:   -> wi 4   F/wnf 1471   E.wex 1503

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-gen 1460  ax-ie2 1505  ax-4 1521

This theorem depends on definitions:  df-bi 117  df-nf 1472

This theorem is referenced by:  19.36i  1683  cbvexv1  1763  euexex  2127  ceqsex  2798  sbhypf  2810  vtoclgf  2819  vtoclg1f  2820  vtoclef  2834  copsexg  4274  copsex2g  4276  ralxpf  4809  rexxpf  4810  dmcoss  4932  fv3  5578  tz6.12c  5585  0neqopab  5964  cnvoprab  6289  bj-exlimmpi  15332