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Theorem dfvd3an 39127
Description: Definition of a 3-hypothesis virtual deduction in vd conjunction form. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dfvd3an ((   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   ) ↔ ((𝜑𝜓𝜒) → 𝜃))

Proof of Theorem dfvd3an
StepHypRef Expression
1 df-vd1 39103 . 2 ((   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   ) ↔ ((   𝜑   ,   𝜓   ,   𝜒   )𝜃))
2 df-vhc3 39122 . . 3 ((   𝜑   ,   𝜓   ,   𝜒   ) ↔ (𝜑𝜓𝜒))
32imbi1i 338 . 2 (((   𝜑   ,   𝜓   ,   𝜒   )𝜃) ↔ ((𝜑𝜓𝜒) → 𝜃))
41, 3bitri 264 1 ((   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   ) ↔ ((𝜑𝜓𝜒) → 𝜃))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  w3a 1054  (   wvd1 39102  (   wvhc3 39121
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-vd1 39103  df-vhc3 39122
This theorem is referenced by:  dfvd3ani  39128  dfvd3anir  39129
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