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Theorem bibi1i 217
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 128 . 2 ((φχ) ↔ (χφ))
2 bibi.a . . 3 (φψ)
32bibi2i 216 . 2 ((χφ) ↔ (χψ))
4 bicom 128 . 2 ((χψ) ↔ (ψχ))
51, 3, 43bitri 195 1 ((φχ) ↔ (ψχ))
Colors of variables: wff set class
Syntax hints:  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:  bibi12i  218  bilukdc  1270  sbrbis  1817  necon1abiddc  2245  necon1bbiddc  2246  necon4abiddc  2256  elrab3t  2674  ssequn1  3090  asymref  4637
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