Theorem e33

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

	Ref	Expression
Hypotheses	e33.1	|- (. ph ,. ps ,. ch ->. th ).
	e33.2	|- (. ph ,. ps ,. ch ->. ta ).
	e33.3	|- ( th -> ( ta -> et ) )
Assertion	e33	|- (. ph ,. ps ,. ch ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e33.1	|- (. ph ,. ps ,. ch ->. th ).
2		e33.2	|- (. ph ,. ps ,. ch ->. ta ).
3		e33.3	|- ( th -> ( ta -> et ) )
4	3	a1i	|- ( th -> ( th -> ( ta -> et ) ) )
5	1 1 2 4	e333	|- (. ph ,. ps ,. ch ->. et ).