Theorem e022

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

	Ref	Expression
Hypotheses	e022.1	|- ph
	e022.2	|- (. ps ,. ch ->. th ).
	e022.3	|- (. ps ,. ch ->. ta ).
	e022.4	|- ( ph -> ( th -> ( ta -> et ) ) )
Assertion	e022	|- (. ps ,. ch ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e022.1	|- ph
2		e022.2	|- (. ps ,. ch ->. th ).
3		e022.3	|- (. ps ,. ch ->. ta ).
4		e022.4	|- ( ph -> ( th -> ( ta -> et ) ) )
5	1	vd02	|- (. ps ,. ch ->. ph ).
6	5 2 3 4	e222	|- (. ps ,. ch ->. et ).