Theorem e201

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

	Ref	Expression
Hypotheses	e201.1	|- (. ph ,. ps ->. ch ).
	e201.2	|- th
	e201.3	|- (. ph ->. ta ).
	e201.4	|- ( ch -> ( th -> ( ta -> et ) ) )
Assertion	e201	|- (. ph ,. ps ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e201.1	|- (. ph ,. ps ->. ch ).
2		e201.2	|- th
3		e201.3	|- (. ph ->. ta ).
4		e201.4	|- ( ch -> ( th -> ( ta -> et ) ) )
5	2	vd01	|- (. ph ->. th ).
6	1 5 3 4	e211	|- (. ph ,. ps ->. et ).