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Theorem bibi1i 226
Description: Inference adding a biconditional to the right in an equivalence. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
bibi.a (𝜑𝜓)
Assertion
Ref Expression
bibi1i ((𝜑𝜒) ↔ (𝜓𝜒))

Proof of Theorem bibi1i
StepHypRef Expression
1 bicom 138 . 2 ((𝜑𝜒) ↔ (𝜒𝜑))
2 bibi.a . . 3 (𝜑𝜓)
32bibi2i 225 . 2 ((𝜒𝜑) ↔ (𝜒𝜓))
4 bicom 138 . 2 ((𝜒𝜓) ↔ (𝜓𝜒))
51, 3, 43bitri 204 1 ((𝜑𝜒) ↔ (𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  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:  bibi12i  227  bilukdc  1330  sbrbis  1880  necon1abiddc  2313  necon1bbiddc  2314  necon4abiddc  2324  elrab3t  2761  ddifstab  3121  ssequn1  3159  asymref  4780
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