Theorem e21

Description: A virtual deduction elimination rule (see syl6ci ). (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e21.1	|- (. ph ,. ps ->. ch ).
	e21.2	|- (. ph ->. th ).
	e21.3	|- ( ch -> ( th -> ta ) )
Assertion	e21	|- (. ph ,. ps ->. ta ).

Proof

Step	Hyp	Ref	Expression
1		e21.1	|- (. ph ,. ps ->. ch ).
2		e21.2	|- (. ph ->. th ).
3		e21.3	|- ( ch -> ( th -> ta ) )
4	2	vd12	|- (. ph ,. ps ->. th ).
5	1 4 3	e22	|- (. ph ,. ps ->. ta ).