Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e3bir Structured version   Visualization version   GIF version

Theorem e3bir 39283
Description: Right biconditional form of e3 39281. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e3bir.1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
e3bir.2 (𝜏𝜃)
Assertion
Ref Expression
e3bir (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )

Proof of Theorem e3bir
StepHypRef Expression
1 e3bir.1 . 2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
2 e3bir.2 . . 3 (𝜏𝜃)
32biimpri 218 . 2 (𝜃𝜏)
41, 3e3 39281 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )
Colors of variables: wff setvar class
Syntax hints:  wb 196  (   wvd3 39120
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-an 385  df-3an 1056  df-vd3 39123
This theorem is referenced by:  en3lplem2VD  39393
  Copyright terms: Public domain W3C validator