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Theorem e323 39518
 Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 17-Apr-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e323.1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
e323.2 (   𝜑   ,   𝜓   ▶   𝜏   )
e323.3 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )
e323.4 (𝜃 → (𝜏 → (𝜂𝜁)))
Assertion
Ref Expression
e323 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜁   )

Proof of Theorem e323
StepHypRef Expression
1 e323.1 . . . 4 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
21dfvd3i 39333 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
3 e323.2 . . . 4 (   𝜑   ,   𝜓   ▶   𝜏   )
43dfvd2i 39326 . . 3 (𝜑 → (𝜓𝜏))
5 e323.3 . . . 4 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )
65dfvd3i 39333 . . 3 (𝜑 → (𝜓 → (𝜒𝜂)))
7 e323.4 . . 3 (𝜃 → (𝜏 → (𝜂𝜁)))
82, 4, 6, 7ee323 39239 . 2 (𝜑 → (𝜓 → (𝜒𝜁)))
98dfvd3ir 39334 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜁   )
 Colors of variables: wff setvar class Syntax hints:   → wi 4  (   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:  trintALTVD  39638
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