Theorem e33an

Description: Conjunction form of e33 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e33an.1	|- (. ph ,. ps ,. ch ->. th ).
	e33an.2	|- (. ph ,. ps ,. ch ->. ta ).
	e33an.3	|- ( ( th /\ ta ) -> et )
Assertion	e33an	|- (. ph ,. ps ,. ch ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e33an.1	|- (. ph ,. ps ,. ch ->. th ).
2		e33an.2	|- (. ph ,. ps ,. ch ->. ta ).
3		e33an.3	|- ( ( th /\ ta ) -> et )
4	3	ex	|- ( th -> ( ta -> et ) )
5	1 2 4	e33	|- (. ph ,. ps ,. ch ->. et ).