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Theorem bibi12i 328
 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 326 . 2 ((𝜑𝜒) ↔ (𝜑𝜃))
3 bibi2i.1 . . 3 (𝜑𝜓)
43bibi1i 327 . 2 ((𝜑𝜃) ↔ (𝜓𝜃))
52, 4bitri 264 1 ((𝜑𝜒) ↔ (𝜓𝜃))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 196 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 197 This theorem is referenced by:  pm5.32  671  orbidi  1011  pm5.7  1013  xorbi12i  1626  abbi  2875  brsymdif  4863  nfnid  5046  asymref  5670  isocnv2  6745  zfcndrep  9648  f1omvdco3  18089  brtxpsd  32328  bj-sbeq  33218  symrefref3  34651  rp-fakeoranass  38379  rp-fakeinunass  38381  relexp0eq  38513
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