Theorem e32

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

	Ref	Expression
Hypotheses	e32.1	|- (. ph ,. ps ,. ch ->. th ).
	e32.2	|- (. ph ,. ps ->. ta ).
	e32.3	|- ( th -> ( ta -> et ) )
Assertion	e32	|- (. ph ,. ps ,. ch ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e32.1	|- (. ph ,. ps ,. ch ->. th ).
2		e32.2	|- (. ph ,. ps ->. ta ).
3		e32.3	|- ( th -> ( ta -> et ) )
4	2	vd23	|- (. ph ,. ps ,. ch ->. ta ).
5	1 4 3	e33	|- (. ph ,. ps ,. ch ->. et ).