Theorem e03

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e03.1	|- ph
	e03.2	|- (. ps ,. ch ,. th ->. ta ).
	e03.3	|- ( ph -> ( ta -> et ) )
Assertion	e03	|- (. ps ,. ch ,. th ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e03.1	|- ph
2		e03.2	|- (. ps ,. ch ,. th ->. ta ).
3		e03.3	|- ( ph -> ( ta -> et ) )
4	1	vd03	|- (. ps ,. ch ,. th ->. ph ).
5	4 2 3	e33	|- (. ps ,. ch ,. th ->. et ).