Theorem ee11an

Description: e11an without virtual deductions. syl22anc is also e11an without virtual deductions, exept with a different order of hypotheses. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee11an.1	|- ( ph -> ps )
	ee11an.2	|- ( ph -> ch )
	ee11an.3	|- ( ( ps /\ ch ) -> th )
Assertion	ee11an	|- ( ph -> th )

Proof

Step	Hyp	Ref	Expression
1		ee11an.1	|- ( ph -> ps )
2		ee11an.2	|- ( ph -> ch )
3		ee11an.3	|- ( ( ps /\ ch ) -> th )
4	3	ex	|- ( ps -> ( ch -> th ) )
5	1 2 4	sylc	|- ( ph -> th )