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Theorem bibi12i 228
Description: The equivalence of two equivalences. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
bibi.a (𝜑𝜓)
bibi12.2 (𝜒𝜃)
Assertion
Ref Expression
bibi12i ((𝜑𝜒) ↔ (𝜓𝜃))

Proof of Theorem bibi12i
StepHypRef Expression
1 bibi12.2 . . 3 (𝜒𝜃)
21bibi2i 226 . 2 ((𝜑𝜒) ↔ (𝜑𝜃))
3 bibi.a . . 3 (𝜑𝜓)
43bibi1i 227 . 2 ((𝜑𝜃) ↔ (𝜓𝜃))
52, 4bitri 183 1 ((𝜑𝜒) ↔ (𝜓𝜃))
Colors of variables: wff set class
Syntax hints:  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  pm5.7dc  923  asymref  4894  rexrnmpt  5531  uzennn  10177
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