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Theorem vd12 42220
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 (   𝜑   ▶   𝜓   )
Assertion
Ref Expression
vd12 (   𝜑   ,   𝜒   ▶   𝜓   )

Proof of Theorem vd12
StepHypRef Expression
1 vd12.1 . . . 4 (   𝜑   ▶   𝜓   )
21in1 42191 . . 3 (𝜑𝜓)
32a1d 25 . 2 (𝜑 → (𝜒𝜓))
43dfvd2ir 42206 1 (   𝜑   ,   𝜒   ▶   𝜓   )
Colors of variables: wff setvar class
Syntax hints:  (   wvd1 42189  (   wvd2 42197
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 206  df-an 397  df-vd1 42190  df-vd2 42198
This theorem is referenced by:  e221  42269  e212  42271  e122  42273  e112  42274  e121  42276  e211  42277  e120  42283  e12  42344  e21  42350
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