Theorem e112

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e112.1	|- (. ph ->. ps ).
	e112.2	|- (. ph ->. ch ).
	e112.3	|- (. ph ,. th ->. ta ).
	e112.4	|- ( ps -> ( ch -> ( ta -> et ) ) )
Assertion	e112	|- (. ph ,. th ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e112.1	|- (. ph ->. ps ).
2		e112.2	|- (. ph ->. ch ).
3		e112.3	|- (. ph ,. th ->. ta ).
4		e112.4	|- ( ps -> ( ch -> ( ta -> et ) ) )
5	1	vd12	|- (. ph ,. th ->. ps ).
6	2	vd12	|- (. ph ,. th ->. ch ).
7	5 6 3 4	e222	|- (. ph ,. th ->. et ).