Theorem vd12 38825

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 an additional hypothesis. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
vd12.1	|- (. ph ->. ps ).

Assertion

Ref	Expression
vd12	|- (. ph ,. ch ->. ps ).

Proof of Theorem vd12

Step	Hyp	Ref	Expression
1		vd12.1	. . . 4 |- (. ph ->. ps ).
2	1	in1 38787	. . 3 |- ( ph -> ps )
3	2	a1d 25	. 2 |- ( ph -> ( ch -> ps ) )
4	3	dfvd2ir 38802	1 |- (. ph ,. ch ->. ps ).

Syntax hints:   (.wvd1 38785   (.wvd2 38793

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-vd1 38786  df-vd2 38794

This theorem is referenced by:  e221  38874  e212  38876  e122  38878  e112  38879  e121  38881  e211  38882  e120  38888  e12  38951  e21  38957