Theorem e212

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

	Ref	Expression
Hypotheses	e212.1	|- (. ph ,. ps ->. ch ).
	e212.2	|- (. ph ->. th ).
	e212.3	|- (. ph ,. ps ->. ta ).
	e212.4	|- ( ch -> ( th -> ( ta -> et ) ) )
Assertion	e212	|- (. ph ,. ps ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e212.1	|- (. ph ,. ps ->. ch ).
2		e212.2	|- (. ph ->. th ).
3		e212.3	|- (. ph ,. ps ->. ta ).
4		e212.4	|- ( ch -> ( th -> ( ta -> et ) ) )
5	2	vd12	|- (. ph ,. ps ->. th ).
6	1 5 3 4	e222	|- (. ph ,. ps ->. et ).