Theorem vd13

Description: A virtual deduction with 1 virtual hypothesis virtually inferring a virtual conclusion infers that the same conclusion is virtually inferred by the same virtual hypothesis and a two additional hypotheses. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	vd13.1	|- (. ph ->. ps ).
Assertion	vd13	|- (. ph ,. ch ,. th ->. ps ).

Proof

Step	Hyp	Ref	Expression
1		vd13.1	|- (. ph ->. ps ).
2	1	in1	|- ( ph -> ps )
3	2	a1d	|- ( ph -> ( ch -> ps ) )
4	3	a1dd	|- ( ph -> ( ch -> ( th -> ps ) ) )
5	4	dfvd3ir	|- (. ph ,. ch ,. th ->. ps ).