Theorem eexinst11

Description: exinst11 without virtual deductions. (Contributed by Alan Sare, 21-Apr-2013) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	eexinst11.1	|- ( ph -> E. x ps )
	eexinst11.2	|- ( ph -> ( ps -> ch ) )
	eexinst11.3	|- ( ph -> A. x ph )
	eexinst11.4	|- ( ch -> A. x ch )
Assertion	eexinst11	|- ( ph -> ch )

Proof

Step	Hyp	Ref	Expression
1		eexinst11.1	|- ( ph -> E. x ps )
2		eexinst11.2	|- ( ph -> ( ps -> ch ) )
3		eexinst11.3	|- ( ph -> A. x ph )
4		eexinst11.4	|- ( ch -> A. x ch )
5	3 4 2	exlimdh	|- ( ph -> ( E. x ps -> ch ) )
6	1 5	syl5com	|- ( ph -> ( ph -> ch ) )
7	6	pm2.43i	|- ( ph -> ch )