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Theorem dfvd2an 41740
Description: Definition of a 2-hypothesis virtual deduction in vd conjunction form. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dfvd2an ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((𝜑𝜓) → 𝜒))

Proof of Theorem dfvd2an
StepHypRef Expression
1 df-vd1 41728 . 2 ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((   𝜑   ,   𝜓   )𝜒))
2 df-vhc2 41739 . . 3 ((   𝜑   ,   𝜓   ) ↔ (𝜑𝜓))
32imbi1i 353 . 2 (((   𝜑   ,   𝜓   )𝜒) ↔ ((𝜑𝜓) → 𝜒))
41, 3bitri 278 1 ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((𝜑𝜓) → 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wa 399  (   wvd1 41727  (   wvhc2 41738
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-vd1 41728  df-vhc2 41739
This theorem is referenced by:  dfvd2ani  41741  dfvd2anir  41742  iden2  41772
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