Theorem e32an

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e32an.1	|- (. ph ,. ps ,. ch ->. th ).
	e32an.2	|- (. ph ,. ps ->. ta ).
	e32an.3	|- ( ( th /\ ta ) -> et )
Assertion	e32an	|- (. ph ,. ps ,. ch ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e32an.1	|- (. ph ,. ps ,. ch ->. th ).
2		e32an.2	|- (. ph ,. ps ->. ta ).
3		e32an.3	|- ( ( th /\ ta ) -> et )
4	3	ex	|- ( th -> ( ta -> et ) )
5	1 2 4	e32	|- (. ph ,. ps ,. ch ->. et ).