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Theorem bibi12i 327
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 325 . 2 ((𝜑𝜒) ↔ (𝜑𝜃))
3 bibi2i.1 . . 3 (𝜑𝜓)
43bibi1i 326 . 2 ((𝜑𝜃) ↔ (𝜓𝜃))
52, 4bitri 262 1 ((𝜑𝜒) ↔ (𝜓𝜃))
Colors of variables: wff setvar class
Syntax hints:  wb 194
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 195
This theorem is referenced by:  pm5.32  665  orbidi  968  pm5.7  970  xorbi12i  1468  abbi  2723  brsymdif  4635  nfnid  4818  asymref  5418  isocnv2  6459  zfcndrep  9292  f1omvdco3  17638  brtxpsd  30977  bj-sbeq  31884  rp-fakeoranass  36674  rp-fakeinunass  36676  relexp0eq  36808
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