Theorem exlimd 1650

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 1572	. 2 |- ( ph -> A. x ph )
3		exlimd.2	. . 3 |- F/ x ch
4	3	nfri 1572	. 2 |- ( ch -> A. x ch )
5		exlimd.3	. 2 |- ( ph -> ( ps -> ch ) )
6	2, 4, 5	exlimdh 1649	1 |- ( ph -> ( E. x ps -> ch ) )

This proof depends on syntax axioms:   -> wi 4   F/wnf 1513   E.wex 1545

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-5 1500  ax-gen 1502  ax-ie2 1547  ax-4 1563

This proof depends on definitions:  df-bi 117  df-nf 1514

This theorem is used by:  exlimdd  1925  ceqsalg  2850  copsex2t  4385  alxfr  4607  mosubopt  4840  ovmpodf  6220  ovi3  6226  fsum2dlemstep  12201  fprod2dlemstep  12389  lss1d  14720  bj-exlimmp  16797