Theorem exlimexi

Description: Inference similar to Theorem 19.23 of Margaris p. 90. (Contributed by Alan Sare, 21-Apr-2013) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	exlimexi.1	|- ( ps -> A. x ps )
	exlimexi.2	|- ( E. x ph -> ( ph -> ps ) )
Assertion	exlimexi	|- ( E. x ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		exlimexi.1	|- ( ps -> A. x ps )
2		exlimexi.2	|- ( E. x ph -> ( ph -> ps ) )
3		hbe1	|- ( E. x ph -> A. x E. x ph )
4	3 1 2	exlimdh	|- ( E. x ph -> ( E. x ph -> ps ) )
5	4	pm2.43i	|- ( E. x ph -> ps )