Theorem e20

Description: A virtual deduction elimination rule (see syl6mpi ). (Contributed by Alan Sare, 14-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e20.1	|- (. ph ,. ps ->. ch ).
	e20.2	|- th
	e20.3	|- ( ch -> ( th -> ta ) )
Assertion	e20	|- (. ph ,. ps ->. ta ).

Proof

Step	Hyp	Ref	Expression
1		e20.1	|- (. ph ,. ps ->. ch ).
2		e20.2	|- th
3		e20.3	|- ( ch -> ( th -> ta ) )
4	2	vd02	|- (. ph ,. ps ->. th ).
5	1 4 3	e22	|- (. ph ,. ps ->. ta ).