Theorem e23an

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

	Ref	Expression
Hypotheses	e23an.1	|- (. ph ,. ps ->. ch ).
	e23an.2	|- (. ph ,. ps ,. th ->. ta ).
	e23an.3	|- ( ( ch /\ ta ) -> et )
Assertion	e23an	|- (. ph ,. ps ,. th ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e23an.1	|- (. ph ,. ps ->. ch ).
2		e23an.2	|- (. ph ,. ps ,. th ->. ta ).
3		e23an.3	|- ( ( ch /\ ta ) -> et )
4	3	ex	|- ( ch -> ( ta -> et ) )
5	1 2 4	e23	|- (. ph ,. ps ,. th ->. et ).