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Theorem bitr 740
Description: Theorem *4.22 of [WhiteheadRussell] p. 117. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
bitr (((𝜑𝜓) ∧ (𝜓𝜒)) → (𝜑𝜒))

Proof of Theorem bitr
StepHypRef Expression
1 bibi1 339 . 2 ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜓𝜒)))
21biimpar 500 1 (((𝜑𝜓) ∧ (𝜓𝜒)) → (𝜑𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  wa 382
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 195  df-an 384
This theorem is referenced by:  opelopabt  4902  domunfican  8095  albitr  37380  3orbi123VD  37903  e2ebindALT  37983
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