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Theorem biantr 894
Description: A transitive law of equivalence. Compare Theorem *4.22 of [WhiteheadRussell] p. 117. (Contributed by NM, 18-Aug-1993.)
Assertion
Ref Expression
biantr (((𝜑𝜓) ∧ (𝜒𝜓)) → (𝜑𝜒))

Proof of Theorem biantr
StepHypRef Expression
1 id 19 . . 3 ((𝜒𝜓) → (𝜒𝜓))
21bibi2d 230 . 2 ((𝜒𝜓) → ((𝜑𝜒) ↔ (𝜑𝜓)))
32biimparc 293 1 (((𝜑𝜓) ∧ (𝜒𝜓)) → (𝜑𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  bm1.1  2067  bezoutlemmo  10539
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