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Theorem bd3or 9264
 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 (φ ψ χ)

Proof of Theorem bd3or
StepHypRef Expression
1 bd3or.1 . . . 4 BOUNDED φ
2 bd3or.2 . . . 4 BOUNDED ψ
31, 2ax-bdor 9251 . . 3 BOUNDED (φ ψ)
4 bd3or.3 . . 3 BOUNDED χ
53, 4ax-bdor 9251 . 2 BOUNDED ((φ ψ) χ)
6 df-3or 885 . 2 ((φ ψ χ) ↔ ((φ ψ) χ))
75, 6bd0r 9260 1 BOUNDED (φ ψ χ)
 Colors of variables: wff set class Syntax hints:   ∨ wo 628   ∨ w3o 883  BOUNDED wbd 9247 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-bd0 9248  ax-bdor 9251 This theorem depends on definitions:  df-bi 110  df-3or 885 This theorem is referenced by: (None)
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