Theorem e12an

Description: Conjunction form of e12 (see syl6an ). (Contributed by Alan Sare, 11-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e12an.1	|- (. ph ->. ps ).
	e12an.2	|- (. ph ,. ch ->. th ).
	e12an.3	|- ( ( ps /\ th ) -> ta )
Assertion	e12an	|- (. ph ,. ch ->. ta ).

Proof

Step	Hyp	Ref	Expression
1		e12an.1	|- (. ph ->. ps ).
2		e12an.2	|- (. ph ,. ch ->. th ).
3		e12an.3	|- ( ( ps /\ th ) -> ta )
4	3	ex	|- ( ps -> ( th -> ta ) )
5	1 2 4	e12	|- (. ph ,. ch ->. ta ).