Theorem e31

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

	Ref	Expression
Hypotheses	e31.1	|- (. ph ,. ps ,. ch ->. th ).
	e31.2	|- (. ph ->. ta ).
	e31.3	|- ( th -> ( ta -> et ) )
Assertion	e31	|- (. ph ,. ps ,. ch ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e31.1	|- (. ph ,. ps ,. ch ->. th ).
2		e31.2	|- (. ph ->. ta ).
3		e31.3	|- ( th -> ( ta -> et ) )
4	2	vd13	|- (. ph ,. ps ,. ch ->. ta ).
5	1 4 3	e33	|- (. ph ,. ps ,. ch ->. et ).