Theorem e220

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

	Ref	Expression
Hypotheses	e220.1	|- (. ph ,. ps ->. ch ).
	e220.2	|- (. ph ,. ps ->. th ).
	e220.3	|- ta
	e220.4	|- ( ch -> ( th -> ( ta -> et ) ) )
Assertion	e220	|- (. ph ,. ps ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e220.1	|- (. ph ,. ps ->. ch ).
2		e220.2	|- (. ph ,. ps ->. th ).
3		e220.3	|- ta
4		e220.4	|- ( ch -> ( th -> ( ta -> et ) ) )
5	3	vd02	|- (. ph ,. ps ->. ta ).
6	1 2 5 4	e222	|- (. ph ,. ps ->. et ).