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Theorem bicom 139
Description: Commutative law for equivalence. Theorem *4.21 of [WhiteheadRussell] p. 117. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 11-Nov-2012.)
Assertion
Ref Expression
bicom ((𝜑𝜓) ↔ (𝜓𝜑))

Proof of Theorem bicom
StepHypRef Expression
1 bicom1 130 . 2 ((𝜑𝜓) → (𝜓𝜑))
2 bicom1 130 . 2 ((𝜓𝜑) → (𝜑𝜓))
31, 2impbii 125 1 ((𝜑𝜓) ↔ (𝜓𝜑))
Colors of variables: wff set class
Syntax hints:  wb 104
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  bicomd  140  bibi1i  227  bibi1d  232  ibibr  245  bibif  652  con2bidc  810  con2biddc  815  pm5.17dc  851  bigolden  904  nbbndc  1337  bilukdc  1339  falbitru  1360  3impexpbicom  1379  exists1  2051  eqcom  2097  abeq1  2204  necon2abiddc  2328  necon2bbiddc  2329  necon4bbiddc  2336  ssequn1  3185  axpow3  4033  isocnv  5628  bezoutlemle  11439
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