Theorem e002

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

	Ref	Expression
Hypotheses	e002.1	|- ph
	e002.2	|- ps
	e002.3	|- (. ch ,. th ->. ta ).
	e002.4	|- ( ph -> ( ps -> ( ta -> et ) ) )
Assertion	e002	|- (. ch ,. th ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e002.1	|- ph
2		e002.2	|- ps
3		e002.3	|- (. ch ,. th ->. ta ).
4		e002.4	|- ( ph -> ( ps -> ( ta -> et ) ) )
5	1	vd02	|- (. ch ,. th ->. ph ).
6	2	vd02	|- (. ch ,. th ->. ps ).
7	5 6 3 4	e222	|- (. ch ,. th ->. et ).