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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdbi | Unicode version |
Description: A biconditional between two bounded formulas is bounded. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdbi.1 | BOUNDED |
bdbi.2 | BOUNDED |
Ref | Expression |
---|---|
bdbi | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdbi.1 | . . . 4 BOUNDED | |
2 | bdbi.2 | . . . 4 BOUNDED | |
3 | 1, 2 | ax-bdim 10605 | . . 3 BOUNDED |
4 | 2, 1 | ax-bdim 10605 | . . 3 BOUNDED |
5 | 3, 4 | ax-bdan 10606 | . 2 BOUNDED |
6 | dfbi2 380 | . 2 | |
7 | 5, 6 | bd0r 10616 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 BOUNDED wbd 10603 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-bd0 10604 ax-bdim 10605 ax-bdan 10606 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: (None) |
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