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Theorem dfvd3ir 39228
Description: Right-to-left inference form of dfvd3 39226. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
dfvd3ir.1 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
dfvd3ir (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )

Proof of Theorem dfvd3ir
StepHypRef Expression
1 dfvd3ir.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
2 dfvd3 39226 . 2 ((   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   ) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))
31, 2mpbir 221 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd3 39222
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 385  df-3an 1074  df-vd3 39225
This theorem is referenced by:  vd03  39243  vd13  39245  vd23  39246  in3an  39255  idn3  39259  gen31  39265  e223  39279  e333  39379  e233  39411  e323  39412
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