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Theorem bibi12i 341
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 339 . 2 ((𝜑𝜒) ↔ (𝜑𝜃))
3 bibi2i.1 . . 3 (𝜑𝜓)
43bibi1i 340 . 2 ((𝜑𝜃) ↔ (𝜓𝜃))
52, 4bitri 276 1 ((𝜑𝜒) ↔ (𝜓𝜃))
Colors of variables: wff setvar class
Syntax hints:  wb 207
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 208
This theorem is referenced by:  pm5.32  574  biadan  815  orbidi  948  pm5.7  949  xorbi12i  1510  norass  1526  norassOLD  1527  abbiOLD  2960  brsymdif  5122  nfnid  5273  asymref  5974  isocnv2  7076  zfcndrep  10025  f1omvdco3  18497  brtxpsd  33239  bj-sbeq  34102  bj-rcleqf  34221  symrefref3  35667  rp-fakeoranass  39745  rp-fakeinunass  39746  relexp0eq  39911  absnsb  43128  ichcom  43449  ichbi12i  43450
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