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Theorem bibi1i 227
 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 139 . 2 ((𝜑𝜒) ↔ (𝜒𝜑))
2 bibi.a . . 3 (𝜑𝜓)
32bibi2i 226 . 2 ((𝜒𝜑) ↔ (𝜒𝜓))
4 bicom 139 . 2 ((𝜒𝜓) ↔ (𝜓𝜒))
51, 3, 43bitri 205 1 ((𝜑𝜒) ↔ (𝜓𝜒))
 Colors of variables: wff set class Syntax hints:   ↔ wb 104 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107 This theorem depends on definitions:  df-bi 116 This theorem is referenced by:  bibi12i  228  biadani  602  bilukdc  1375  sbrbis  1929  necon1abiddc  2372  necon1bbiddc  2373  necon4abiddc  2383  elrab3t  2845  ddifstab  3215  ssequn1  3253  asymref  4936
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