Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  dfvd2an Structured version   Visualization version   GIF version

Theorem dfvd2an 39323
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 39311 . 2 ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((   𝜑   ,   𝜓   )𝜒))
2 df-vhc2 39322 . . 3 ((   𝜑   ,   𝜓   ) ↔ (𝜑𝜓))
32imbi1i 338 . 2 (((   𝜑   ,   𝜓   )𝜒) ↔ ((𝜑𝜓) → 𝜒))
41, 3bitri 264 1 ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((𝜑𝜓) → 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 382  (   wvd1 39310  (   wvhc2 39321
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 39311  df-vhc2 39322
This theorem is referenced by:  dfvd2ani  39324  dfvd2anir  39325  iden2  39364
  Copyright terms: Public domain W3C validator