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Theorem bd0r 9945
 Description: A formula equivalent to a bounded one is bounded. Stated with a commuted (compared with bd0 9944) biconditional in the hypothesis, to work better with definitions ( is the definiendum that one wants to prove bounded). (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bd0r.min BOUNDED
bd0r.maj
Assertion
Ref Expression
bd0r BOUNDED

Proof of Theorem bd0r
StepHypRef Expression
1 bd0r.min . 2 BOUNDED
2 bd0r.maj . . 3
32bicomi 123 . 2
41, 3bd0 9944 1 BOUNDED
 Colors of variables: wff set class Syntax hints:   wb 98  BOUNDED wbd 9932 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 9933 This theorem depends on definitions:  df-bi 110 This theorem is referenced by:  bdbi  9946  bdstab  9947  bddc  9948  bd3or  9949  bd3an  9950  bdfal  9953  bdxor  9956  bj-bdcel  9957  bdab  9958  bdcdeq  9959  bdne  9973  bdnel  9974  bdreu  9975  bdrmo  9976  bdsbcALT  9979  bdss  9984  bdeq0  9987  bdvsn  9994  bdop  9995  bdeqsuc  10001  bj-bdind  10054
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