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Theorem biantr 858
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 221 . 2 ((χψ) → ((φχ) ↔ (φψ)))
32biimparc 283 1 (((φψ) (χψ)) → (φχ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  bm1.1  2022
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