Theorem e13an

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

	Ref	Expression
Hypotheses	e13an.1	|- (. ph ->. ps ).
	e13an.2	|- (. ph ,. ch ,. th ->. ta ).
	e13an.3	|- ( ( ps /\ ta ) -> et )
Assertion	e13an	|- (. ph ,. ch ,. th ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e13an.1	|- (. ph ->. ps ).
2		e13an.2	|- (. ph ,. ch ,. th ->. ta ).
3		e13an.3	|- ( ( ps /\ ta ) -> et )
4	3	ex	|- ( ps -> ( ta -> et ) )
5	1 2 4	e13	|- (. ph ,. ch ,. th ->. et ).