Theorem e121

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

	Ref	Expression
Hypotheses	e121.1	|- (. ph ->. ps ).
	e121.2	|- (. ph ,. ch ->. th ).
	e121.3	|- (. ph ->. ta ).
	e121.4	|- ( ps -> ( th -> ( ta -> et ) ) )
Assertion	e121	|- (. ph ,. ch ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e121.1	|- (. ph ->. ps ).
2		e121.2	|- (. ph ,. ch ->. th ).
3		e121.3	|- (. ph ->. ta ).
4		e121.4	|- ( ps -> ( th -> ( ta -> et ) ) )
5	1	vd12	|- (. ph ,. ch ->. ps ).
6	3	vd12	|- (. ph ,. ch ->. ta ).
7	5 2 6 4	e222	|- (. ph ,. ch ->. et ).