Theorem e102

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

	Ref	Expression
Hypotheses	e102.1	|- (. ph ->. ps ).
	e102.2	|- ch
	e102.3	|- (. ph ,. th ->. ta ).
	e102.4	|- ( ps -> ( ch -> ( ta -> et ) ) )
Assertion	e102	|- (. ph ,. th ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e102.1	|- (. ph ->. ps ).
2		e102.2	|- ch
3		e102.3	|- (. ph ,. th ->. ta ).
4		e102.4	|- ( ps -> ( ch -> ( ta -> et ) ) )
5	2	vd01	|- (. ph ->. ch ).
6	1 5 3 4	e112	|- (. ph ,. th ->. et ).