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Theorem bibi12i 227
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 225 . 2 ((𝜑𝜒) ↔ (𝜑𝜃))
3 bibi.a . . 3 (𝜑𝜓)
43bibi1i 226 . 2 ((𝜑𝜃) ↔ (𝜓𝜃))
52, 4bitri 182 1 ((𝜑𝜒) ↔ (𝜓𝜃))
Colors of variables: wff set class
Syntax hints:  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  pm5.7dc  896  asymref  4740  rexrnmpt  5342
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