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Theorem vd12 39345
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 39307 . . 3 (𝜑𝜓)
32a1d 25 . 2 (𝜑 → (𝜒𝜓))
43dfvd2ir 39322 1 (   𝜑   ,   𝜒   ▶   𝜓   )
Colors of variables: wff setvar class
Syntax hints:  (   wvd1 39305  (   wvd2 39313
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 385  df-vd1 39306  df-vd2 39314
This theorem is referenced by:  e221  39394  e212  39396  e122  39398  e112  39399  e121  39401  e211  39402  e120  39408  e12  39471  e21  39477
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