Theorem e11an

Description: Conjunction form of e11 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e11an.1	|- (. ph ->. ps ).
	e11an.2	|- (. ph ->. ch ).
	e11an.3	|- ( ( ps /\ ch ) -> th )
Assertion	e11an	|- (. ph ->. th ).

Proof

Step	Hyp	Ref	Expression
1		e11an.1	|- (. ph ->. ps ).
2		e11an.2	|- (. ph ->. ch ).
3		e11an.3	|- ( ( ps /\ ch ) -> th )
4	3	ex	|- ( ps -> ( ch -> th ) )
5	1 2 4	e11	|- (. ph ->. th ).