MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  bitr Structured version   Visualization version   GIF version

Theorem bitr 802
Description: Theorem *4.22 of [WhiteheadRussell] p. 117. bitri 274 in closed form. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
bitr (((𝜑𝜓) ∧ (𝜓𝜒)) → (𝜑𝜒))

Proof of Theorem bitr
StepHypRef Expression
1 bibi1 352 . 2 ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜓𝜒)))
21biimpar 478 1 (((𝜑𝜓) ∧ (𝜓𝜒)) → (𝜑𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wa 396
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
This theorem is referenced by:  opelopabt  5448  domunfican  9075  albitr  41963  3orbi123VD  42452  e2ebindALT  42531
  Copyright terms: Public domain W3C validator