Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  dfvd2 Structured version   Visualization version   GIF version

Theorem dfvd2 42199
Description: Definition of a 2-hypothesis virtual deduction. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dfvd2 ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓𝜒)))

Proof of Theorem dfvd2
StepHypRef Expression
1 df-vd2 42198 . 2 ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ ((𝜑𝜓) → 𝜒))
2 impexp 451 . 2 (((𝜑𝜓) → 𝜒) ↔ (𝜑 → (𝜓𝜒)))
31, 2bitri 274 1 ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wa 396  (   wvd2 42197
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 206  df-an 397  df-vd2 42198
This theorem is referenced by:  dfvd2i  42205  dfvd2ir  42206  dfvd2imp  42223  dfvd2impr  42224
  Copyright terms: Public domain W3C validator