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Theorem vd13 38294
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 a two additional hypotheses. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
vd13.1 (   𝜑   ▶   𝜓   )
Assertion
Ref Expression
vd13 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜓   )

Proof of Theorem vd13
StepHypRef Expression
1 vd13.1 . . . . 5 (   𝜑   ▶   𝜓   )
21in1 38255 . . . 4 (𝜑𝜓)
32a1d 25 . . 3 (𝜑 → (𝜒𝜓))
43a1dd 50 . 2 (𝜑 → (𝜒 → (𝜃𝜓)))
54dfvd3ir 38277 1 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜓   )
Colors of variables: wff setvar class
Syntax hints:  (   wvd1 38253  (   wvd3 38271
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-3an 1038  df-vd1 38254  df-vd3 38274
This theorem is referenced by:  e13  38443  e31  38446  e123  38457
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