Theorem e021

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

	Ref	Expression
Hypotheses	e021.1	|- ph
	e021.2	|- (. ps ,. ch ->. th ).
	e021.3	|- (. ps ->. ta ).
	e021.4	|- ( ph -> ( th -> ( ta -> et ) ) )
Assertion	e021	|- (. ps ,. ch ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e021.1	|- ph
2		e021.2	|- (. ps ,. ch ->. th ).
3		e021.3	|- (. ps ->. ta ).
4		e021.4	|- ( ph -> ( th -> ( ta -> et ) ) )
5	1	vd01	|- (. ps ->. ph ).
6	5 2 3 4	e121	|- (. ps ,. ch ->. et ).