Theorem vd13 38826

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.)

Hypothesis

Ref	Expression
vd13.1	|- (. ph ->. ps ).

Assertion

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

Proof of Theorem vd13

Step	Hyp	Ref	Expression
1		vd13.1	. . . . 5 |- (. ph ->. ps ).
2	1	in1 38787	. . . 4 |- ( ph -> ps )
3	2	a1d 25	. . 3 |- ( ph -> ( ch -> ps ) )
4	3	a1dd 50	. 2 |- ( ph -> ( ch -> ( th -> ps ) ) )
5	4	dfvd3ir 38809	1 |- (. ph ,. ch ,. th ->. ps ).

Syntax hints:   (.wvd1 38785   (.wvd3 38803

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039  df-vd1 38786  df-vd3 38806

This theorem is referenced by:  e13  38975  e31  38978  e123  38989