Theorem e30

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

	Ref	Expression
Hypotheses	e30.1	|- (. ph ,. ps ,. ch ->. th ).
	e30.2	|- ta
	e30.3	|- ( th -> ( ta -> et ) )
Assertion	e30	|- (. ph ,. ps ,. ch ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e30.1	|- (. ph ,. ps ,. ch ->. th ).
2		e30.2	|- ta
3		e30.3	|- ( th -> ( ta -> et ) )
4	2	vd03	|- (. ph ,. ps ,. ch ->. ta ).
5	1 4 3	e33	|- (. ph ,. ps ,. ch ->. et ).