Theorem e11

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 14-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e11.1	|- (. ph ->. ps ).
	e11.2	|- (. ph ->. ch ).
	e11.3	|- ( ps -> ( ch -> th ) )
Assertion	e11	|- (. ph ->. th ).

Proof

Step	Hyp	Ref	Expression
1		e11.1	|- (. ph ->. ps ).
2		e11.2	|- (. ph ->. ch ).
3		e11.3	|- ( ps -> ( ch -> th ) )
4	3	a1i	|- ( ps -> ( ps -> ( ch -> th ) ) )
5	1 1 2 4	e111	|- (. ph ->. th ).