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Theorem bibi12i 331
Description: The equivalence of two equivalences. (Contributed by NM, 26-May-1993.)
Hypotheses
Ref Expression
bibi2i.1 (𝜑𝜓)
bibi12i.2 (𝜒𝜃)
Assertion
Ref Expression
bibi12i ((𝜑𝜒) ↔ (𝜓𝜃))

Proof of Theorem bibi12i
StepHypRef Expression
1 bibi12i.2 . . 3 (𝜒𝜃)
21bibi2i 329 . 2 ((𝜑𝜒) ↔ (𝜑𝜃))
3 bibi2i.1 . . 3 (𝜑𝜓)
43bibi1i 330 . 2 ((𝜑𝜃) ↔ (𝜓𝜃))
52, 4bitri 267 1 ((𝜑𝜒) ↔ (𝜓𝜃))
Colors of variables: wff setvar class
Syntax hints:  wb 198
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 199
This theorem is referenced by:  pm5.32  569  biadan  853  orbidi  980  pm5.7  981  xorbi12i  1650  abbi  2942  brsymdif  4934  nfnid  5077  asymref  5758  isocnv2  6841  zfcndrep  9758  f1omvdco3  18226  brtxpsd  32535  bj-sbeq  33412  symrefref3  34853  rp-fakeoranass  38696  rp-fakeinunass  38697  relexp0eq  38829  absnsb  41957
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