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Theorem vd12 41240
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 41211 . . 3 (𝜑𝜓)
32a1d 25 . 2 (𝜑 → (𝜒𝜓))
43dfvd2ir 41226 1 (   𝜑   ,   𝜒   ▶   𝜓   )
Colors of variables: wff setvar class
Syntax hints:  (   wvd1 41209  (   wvd2 41217
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 210  df-an 400  df-vd1 41210  df-vd2 41218
This theorem is referenced by:  e221  41289  e212  41291  e122  41293  e112  41294  e121  41296  e211  41297  e120  41303  e12  41364  e21  41370
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