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Theorem vd23 39352
Description: A virtual deduction with 2 virtual hypotheses virtually inferring a virtual conclusion infers that the same conclusion is virtually inferred by the same 2 virtual hypotheses and a third hypothesis. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
vd23.1 (   𝜑   ,   𝜓   ▶   𝜒   )
Assertion
Ref Expression
vd23 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜒   )

Proof of Theorem vd23
StepHypRef Expression
1 vd23.1 . . . 4 (   𝜑   ,   𝜓   ▶   𝜒   )
21dfvd2i 39326 . . 3 (𝜑 → (𝜓𝜒))
32a1dd 50 . 2 (𝜑 → (𝜓 → (𝜃𝜒)))
43dfvd3ir 39334 1 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜒   )
Colors of variables: wff setvar class
Syntax hints:  (   wvd2 39318  (   wvd3 39328
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 383  df-3an 1073  df-vd2 39319  df-vd3 39331
This theorem is referenced by:  e23  39507  e32  39510  e123  39514
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