Theorem e22

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 2-May-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e22.1	|- (. ph ,. ps ->. ch ).
	e22.2	|- (. ph ,. ps ->. th ).
	e22.3	|- ( ch -> ( th -> ta ) )
Assertion	e22	|- (. ph ,. ps ->. ta ).

Proof

Step	Hyp	Ref	Expression
1		e22.1	|- (. ph ,. ps ->. ch ).
2		e22.2	|- (. ph ,. ps ->. th ).
3		e22.3	|- ( ch -> ( th -> ta ) )
4	3	a1i	|- ( ch -> ( ch -> ( th -> ta ) ) )
5	1 1 2 4	e222	|- (. ph ,. ps ->. ta ).