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Theorem in3an 39498
Description: The virtual deduction introduction rule converting the second conjunct of the third virtual hypothesis into the antecedent of the conclusion. exp4a 422 is the non-virtual deduction form of in3an 39498. (Contributed by Alan Sare, 25-Jun-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
in3an.1 (   𝜑   ,   𝜓   ,   (𝜒𝜃)   ▶   𝜏   )
Assertion
Ref Expression
in3an (   𝜑   ,   𝜓   ,   𝜒   ▶   (𝜃𝜏)   )

Proof of Theorem in3an
StepHypRef Expression
1 in3an.1 . . . 4 (   𝜑   ,   𝜓   ,   (𝜒𝜃)   ▶   𝜏   )
21dfvd3i 39470 . . 3 (𝜑 → (𝜓 → ((𝜒𝜃) → 𝜏)))
32exp4a 422 . 2 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
43dfvd3ir 39471 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   (𝜃𝜏)   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  (   wvd3 39465
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 198  df-an 385  df-3an 1109  df-vd3 39468
This theorem is referenced by:  onfrALTlem2VD  39777
  Copyright terms: Public domain W3C validator