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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdnel | Unicode version |
Description: Non-membership of a setvar in a bounded formula is a bounded formula. (Contributed by BJ, 16-Oct-2019.) |
Ref | Expression |
---|---|
bdnel.1 | BOUNDED |
Ref | Expression |
---|---|
bdnel | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdnel.1 | . . . 4 BOUNDED | |
2 | 1 | bdeli 10637 | . . 3 BOUNDED |
3 | 2 | ax-bdn 10608 | . 2 BOUNDED |
4 | df-nel 2340 | . 2 | |
5 | 3, 4 | bd0r 10616 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wn 3 wcel 1433 wnel 2339 BOUNDED wbd 10603 BOUNDED wbdc 10631 |
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-4 1440 ax-bd0 10604 ax-bdn 10608 |
This theorem depends on definitions: df-bi 115 df-nel 2340 df-bdc 10632 |
This theorem is referenced by: (None) |
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