Theorem e2

Description: A virtual deduction elimination rule. syl6 is e2 without virtual deductions. (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e2.1	|- (. ph ,. ps ->. ch ).
	e2.2	|- ( ch -> th )
Assertion	e2	|- (. ph ,. ps ->. th ).

Proof

Step	Hyp	Ref	Expression
1		e2.1	|- (. ph ,. ps ->. ch ).
2		e2.2	|- ( ch -> th )
3	1	dfvd2i	|- ( ph -> ( ps -> ch ) )
4	3 2	syl6	|- ( ph -> ( ps -> th ) )
5	4	dfvd2ir	|- (. ph ,. ps ->. th ).