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Theorem in3an 41237
 Description: The virtual deduction introduction rule converting the second conjunct of the third virtual hypothesis into the antecedent of the conclusion. exp4a 435 is the non-virtual deduction form of in3an 41237. (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 41218 . . 3 (𝜑 → (𝜓 → ((𝜒𝜃) → 𝜏)))
32exp4a 435 . 2 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
43dfvd3ir 41219 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   (𝜃𝜏)   )
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 399  (   wvd3 41213 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 210  df-an 400  df-3an 1086  df-vd3 41216 This theorem is referenced by:  onfrALTlem2VD  41515
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