Theorem e100

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

	Ref	Expression
Hypotheses	e100.1	|- (. ph ->. ps ).
	e100.2	|- ch
	e100.3	|- th
	e100.4	|- ( ps -> ( ch -> ( th -> ta ) ) )
Assertion	e100	|- (. ph ->. ta ).

Proof

Step	Hyp	Ref	Expression
1		e100.1	|- (. ph ->. ps ).
2		e100.2	|- ch
3		e100.3	|- th
4		e100.4	|- ( ps -> ( ch -> ( th -> ta ) ) )
5	2	vd01	|- (. ph ->. ch ).
6	3	vd01	|- (. ph ->. th ).
7	1 5 6 4	e111	|- (. ph ->. ta ).