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Theorem dfvd2an 37819
 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 37807 . 2 ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((   𝜑   ,   𝜓   )𝜒))
2 df-vhc2 37818 . . 3 ((   𝜑   ,   𝜓   ) ↔ (𝜑𝜓))
32imbi1i 338 . 2 (((   𝜑   ,   𝜓   )𝜒) ↔ ((𝜑𝜓) → 𝜒))
41, 3bitri 263 1 ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((𝜑𝜓) → 𝜒))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 195   ∧ wa 383  (   wvd1 37806  (   wvhc2 37817 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-vhc2 37818 This theorem is referenced by:  dfvd2ani  37820  dfvd2anir  37821  iden2  37860
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