Theorem e211

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

	Ref	Expression
Hypotheses	e211.1	|- (. ph ,. ps ->. ch ).
	e211.2	|- (. ph ->. th ).
	e211.3	|- (. ph ->. ta ).
	e211.4	|- ( ch -> ( th -> ( ta -> et ) ) )
Assertion	e211	|- (. ph ,. ps ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e211.1	|- (. ph ,. ps ->. ch ).
2		e211.2	|- (. ph ->. th ).
3		e211.3	|- (. ph ->. ta ).
4		e211.4	|- ( ch -> ( th -> ( ta -> et ) ) )
5	2	vd12	|- (. ph ,. ps ->. th ).
6	3	vd12	|- (. ph ,. ps ->. ta ).
7	1 5 6 4	e222	|- (. ph ,. ps ->. et ).