Theorem e23

Description: A virtual deduction elimination rule (see syl10 ). (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e23.1	|- (. ph ,. ps ->. ch ).
	e23.2	|- (. ph ,. ps ,. th ->. ta ).
	e23.3	|- ( ch -> ( ta -> et ) )
Assertion	e23	|- (. ph ,. ps ,. th ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e23.1	|- (. ph ,. ps ->. ch ).
2		e23.2	|- (. ph ,. ps ,. th ->. ta ).
3		e23.3	|- ( ch -> ( ta -> et ) )
4	1	vd23	|- (. ph ,. ps ,. th ->. ch ).
5	4 2 3	e33	|- (. ph ,. ps ,. th ->. et ).