Theorem e012

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

	Ref	Expression
Hypotheses	e012.1	|- ph
	e012.2	|- (. ps ->. ch ).
	e012.3	|- (. ps ,. th ->. ta ).
	e012.4	|- ( ph -> ( ch -> ( ta -> et ) ) )
Assertion	e012	|- (. ps ,. th ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e012.1	|- ph
2		e012.2	|- (. ps ->. ch ).
3		e012.3	|- (. ps ,. th ->. ta ).
4		e012.4	|- ( ph -> ( ch -> ( ta -> et ) ) )
5	1	vd01	|- (. ps ->. ph ).
6	5 2 3 4	e112	|- (. ps ,. th ->. et ).