Theorem e13

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e13.1	|- (. ph ->. ps ).
	e13.2	|- (. ph ,. ch ,. th ->. ta ).
	e13.3	|- ( ps -> ( ta -> et ) )
Assertion	e13	|- (. ph ,. ch ,. th ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e13.1	|- (. ph ->. ps ).
2		e13.2	|- (. ph ,. ch ,. th ->. ta ).
3		e13.3	|- ( ps -> ( ta -> et ) )
4	1	vd13	|- (. ph ,. ch ,. th ->. ps ).
5	4 2 3	e33	|- (. ph ,. ch ,. th ->. et ).