Theorem vd23

Description: A virtual deduction with 2 virtual hypotheses virtually inferring a virtual conclusion infers that the same conclusion is virtually inferred by the same 2 virtual hypotheses and a third hypothesis. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	vd23.1	|- (. ph ,. ps ->. ch ).
Assertion	vd23	|- (. ph ,. ps ,. th ->. ch ).

Proof

Step	Hyp	Ref	Expression
1		vd23.1	|- (. ph ,. ps ->. ch ).
2	1	dfvd2i	|- ( ph -> ( ps -> ch ) )
3	2	a1dd	|- ( ph -> ( ps -> ( th -> ch ) ) )
4	3	dfvd3ir	|- (. ph ,. ps ,. th ->. ch ).