Metamath Proof Explorer


Theorem vd12

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.)

Ref Expression
Hypothesis vd12.1
|- (. ph ->. ps ).
Assertion vd12
|- (. ph ,. ch ->. ps ).

Proof

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