Theorem e200

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

	Ref	Expression
Hypotheses	e200.1	|- (. ph ,. ps ->. ch ).
	e200.2	|- th
	e200.3	|- ta
	e200.4	|- ( ch -> ( th -> ( ta -> et ) ) )
Assertion	e200	|- (. ph ,. ps ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e200.1	|- (. ph ,. ps ->. ch ).
2		e200.2	|- th
3		e200.3	|- ta
4		e200.4	|- ( ch -> ( th -> ( ta -> et ) ) )
5	2	vd02	|- (. ph ,. ps ->. th ).
6	3	vd02	|- (. ph ,. ps ->. ta ).
7	1 5 6 4	e222	|- (. ph ,. ps ->. et ).