Theorem e21an

Description: Conjunction form of e21 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e21an.1	|- (. ph ,. ps ->. ch ).
	e21an.2	|- (. ph ->. th ).
	e21an.3	|- ( ( ch /\ th ) -> ta )
Assertion	e21an	|- (. ph ,. ps ->. ta ).

Proof

Step	Hyp	Ref	Expression
1		e21an.1	|- (. ph ,. ps ->. ch ).
2		e21an.2	|- (. ph ->. th ).
3		e21an.3	|- ( ( ch /\ th ) -> ta )
4	3	ex	|- ( ch -> ( th -> ta ) )
5	1 2 4	e21	|- (. ph ,. ps ->. ta ).