Theorem e101

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

	Ref	Expression
Hypotheses	e101.1	|- (. ph ->. ps ).
	e101.2	|- ch
	e101.3	|- (. ph ->. th ).
	e101.4	|- ( ps -> ( ch -> ( th -> ta ) ) )
Assertion	e101	|- (. ph ->. ta ).

Proof

Step	Hyp	Ref	Expression
1		e101.1	|- (. ph ->. ps ).
2		e101.2	|- ch
3		e101.3	|- (. ph ->. th ).
4		e101.4	|- ( ps -> ( ch -> ( th -> ta ) ) )
5	2	vd01	|- (. ph ->. ch ).
6	1 5 3 4	e111	|- (. ph ->. ta ).