Theorem exlimd 1557

Description: Deduction from Theorem 19.9 of [Margaris] p. 89. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof rewritten by Jim Kingdon, 18-Jun-2018.)

Hypotheses

Ref	Expression
exlimd.1	|- F/ x ph
exlimd.2	|- F/ x ch
exlimd.3	|- ( ph -> ( ps -> ch ) )

Assertion

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

Proof of Theorem exlimd

Step	Hyp	Ref	Expression
1		exlimd.1	. . 3 |- F/ x ph
2	1	nfri 1480	. 2 |- ( ph -> A. x ph )
3		exlimd.2	. . 3 |- F/ x ch
4	3	nfri 1480	. 2 |- ( ch -> A. x ch )
5		exlimd.3	. 2 |- ( ph -> ( ps -> ch ) )
6	2, 4, 5	exlimdh 1556	1 |- ( ph -> ( E. x ps -> ch ) )

Syntax hints:   -> wi 4   F/wnf 1417   E.wex 1449

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-5 1404  ax-gen 1406  ax-ie2 1451  ax-4 1468

This theorem depends on definitions:  df-bi 116  df-nf 1418

This theorem is referenced by:  exlimdd  1824  ceqsalg  2683  copsex2t  4125  alxfr  4340  mosubopt  4562  ovmpodf  5854  ovi3  5859  fsum2dlemstep  11089  bj-exlimmp  12660