Theorem e011

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

	Ref	Expression
Hypotheses	e011.1	|- ph
	e011.2	|- (. ps ->. ch ).
	e011.3	|- (. ps ->. th ).
	e011.4	|- ( ph -> ( ch -> ( th -> ta ) ) )
Assertion	e011	|- (. ps ->. ta ).

Proof

Step	Hyp	Ref	Expression
1		e011.1	|- ph
2		e011.2	|- (. ps ->. ch ).
3		e011.3	|- (. ps ->. th ).
4		e011.4	|- ( ph -> ( ch -> ( th -> ta ) ) )
5	1	vd01	|- (. ps ->. ph ).
6	5 2 3 4	e111	|- (. ps ->. ta ).