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Mirrors > Home > ILE Home > Th. List > Mathboxes > bd3or | Unicode version |
Description: A disjunction of three bounded formulas is bounded. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bd3or.1 | BOUNDED |
bd3or.2 | BOUNDED |
bd3or.3 | BOUNDED |
Ref | Expression |
---|---|
bd3or | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bd3or.1 | . . . 4 BOUNDED | |
2 | bd3or.2 | . . . 4 BOUNDED | |
3 | 1, 2 | ax-bdor 13560 | . . 3 BOUNDED |
4 | bd3or.3 | . . 3 BOUNDED | |
5 | 3, 4 | ax-bdor 13560 | . 2 BOUNDED |
6 | df-3or 968 | . 2 | |
7 | 5, 6 | bd0r 13569 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wo 698 w3o 966 BOUNDED wbd 13556 |
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 13557 ax-bdor 13560 |
This theorem depends on definitions: df-bi 116 df-3or 968 |
This theorem is referenced by: (None) |
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