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Theorem bitr 805
Description: Theorem *4.22 of [WhiteheadRussell] p. 117. bitri 275 in closed form. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
bitr (((𝜑𝜓) ∧ (𝜓𝜒)) → (𝜑𝜒))

Proof of Theorem bitr
StepHypRef Expression
1 bibi1 351 . 2 ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜓𝜒)))
21biimpar 477 1 (((𝜑𝜓) ∧ (𝜓𝜒)) → (𝜑𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206  wa 395
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 207  df-an 396
This theorem is referenced by:  opelopabt  5542  domunfican  9359  albitr  44359  3orbi123VD  44848  e2ebindALT  44927
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