Theorem exlimii 31426

Description: Inference associated with exlimi 1994. Inferring a theorem when it is implied by an antecedent which may be true. (Contributed by BJ, 15-Sep-2018.)

Hypotheses

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

Assertion

Ref	Expression
exlimii	|- ps

Proof of Theorem exlimii

Step	Hyp	Ref	Expression
1		exlimii.3	. 2 |- E. x ph
2		exlimii.1	. . 3 |- F/ x ps
3		exlimii.2	. . 3 |- ( ph -> ps )
4	2, 3	exlimi 1994	. 2 |- ( E. x ph -> ps )
5	1, 4	ax-mp 5	1 |- ps

Syntax hints:   -> wi 4   E.wex 1662   F/wnf 1666

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-12 1932

This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1663  df-nf 1667

This theorem is referenced by:  exlimiieq1  31429  exlimiieq2  31430