Theorem e1111

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 6-Mar-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e1111.1	|- (. ph ->. ps ).
	e1111.2	|- (. ph ->. ch ).
	e1111.3	|- (. ph ->. th ).
	e1111.4	|- (. ph ->. ta ).
	e1111.5	|- ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) )
Assertion	e1111	|- (. ph ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e1111.1	|- (. ph ->. ps ).
2		e1111.2	|- (. ph ->. ch ).
3		e1111.3	|- (. ph ->. th ).
4		e1111.4	|- (. ph ->. ta ).
5		e1111.5	|- ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) )
6	1	in1	|- ( ph -> ps )
7	2	in1	|- ( ph -> ch )
8	3	in1	|- ( ph -> th )
9	4	in1	|- ( ph -> ta )
10	6 7 8 9 5	ee1111	|- ( ph -> et )
11	10	dfvd1ir	|- (. ph ->. et ).