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Theorem dfvd3anir 37833
Description: Right-to-left inference form of dfvd3an 37831. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
dfvd3anir.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
dfvd3anir (   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   )

Proof of Theorem dfvd3anir
StepHypRef Expression
1 dfvd3anir.1 . 2 ((𝜑𝜓𝜒) → 𝜃)
2 dfvd3an 37831 . 2 ((   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   ) ↔ ((𝜑𝜓𝜒) → 𝜃))
31, 2mpbir 220 1 (   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1031  (   wvd1 37806  (   wvhc3 37825
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 196  df-vd1 37807  df-vhc3 37826
This theorem is referenced by:  el0321old  37963  el123  38012
  Copyright terms: Public domain W3C validator