Theorem e210

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

	Ref	Expression
Hypotheses	e210.1	|- (. ph ,. ps ->. ch ).
	e210.2	|- (. ph ->. th ).
	e210.3	|- ta
	e210.4	|- ( ch -> ( th -> ( ta -> et ) ) )
Assertion	e210	|- (. ph ,. ps ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e210.1	|- (. ph ,. ps ->. ch ).
2		e210.2	|- (. ph ->. th ).
3		e210.3	|- ta
4		e210.4	|- ( ch -> ( th -> ( ta -> et ) ) )
5	3	vd01	|- (. ph ->. ta ).
6	1 2 5 4	e211	|- (. ph ,. ps ->. et ).