Theorem ee22an

Description: e22an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee22an.1	|- ( ph -> ( ps -> ch ) )
	ee22an.2	|- ( ph -> ( ps -> th ) )
	ee22an.3	|- ( ( ch /\ th ) -> ta )
Assertion	ee22an	|- ( ph -> ( ps -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		ee22an.1	|- ( ph -> ( ps -> ch ) )
2		ee22an.2	|- ( ph -> ( ps -> th ) )
3		ee22an.3	|- ( ( ch /\ th ) -> ta )
4	3	ex	|- ( ch -> ( th -> ta ) )
5	1 2 4	syl6c	|- ( ph -> ( ps -> ta ) )