Theorem e110

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

	Ref	Expression
Hypotheses	e110.1	|- (. ph ->. ps ).
	e110.2	|- (. ph ->. ch ).
	e110.3	|- th
	e110.4	|- ( ps -> ( ch -> ( th -> ta ) ) )
Assertion	e110	|- (. ph ->. ta ).

Proof

Step	Hyp	Ref	Expression
1		e110.1	|- (. ph ->. ps ).
2		e110.2	|- (. ph ->. ch ).
3		e110.3	|- th
4		e110.4	|- ( ps -> ( ch -> ( th -> ta ) ) )
5	3	vd01	|- (. ph ->. th ).
6	1 2 5 4	e111	|- (. ph ->. ta ).