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Theorem bd3or 12838
Description: A disjunction of three bounded formulas is bounded. (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bd3or.1 BOUNDED 𝜑
bd3or.2 BOUNDED 𝜓
bd3or.3 BOUNDED 𝜒
Assertion
Ref Expression
bd3or BOUNDED (𝜑𝜓𝜒)

Proof of Theorem bd3or
StepHypRef Expression
1 bd3or.1 . . . 4 BOUNDED 𝜑
2 bd3or.2 . . . 4 BOUNDED 𝜓
31, 2ax-bdor 12825 . . 3 BOUNDED (𝜑𝜓)
4 bd3or.3 . . 3 BOUNDED 𝜒
53, 4ax-bdor 12825 . 2 BOUNDED ((𝜑𝜓) ∨ 𝜒)
6 df-3or 946 . 2 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∨ 𝜒))
75, 6bd0r 12834 1 BOUNDED (𝜑𝜓𝜒)
Colors of variables: wff set class
Syntax hints:  wo 680  w3o 944  BOUNDED wbd 12821
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-bd0 12822  ax-bdor 12825
This theorem depends on definitions:  df-bi 116  df-3or 946
This theorem is referenced by: (None)
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