Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > Mathboxes > bdeq0 | Unicode version |
Description: Boundedness of the formula expressing that a setvar is equal to the empty class. (Contributed by BJ, 21-Nov-2019.) |
Ref | Expression |
---|---|
bdeq0 | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcnul 10656 | . . 3 BOUNDED | |
2 | 1 | bdss 10655 | . 2 BOUNDED |
3 | 0ss 3282 | . . 3 | |
4 | eqss 3014 | . . 3 | |
5 | 3, 4 | mpbiran2 882 | . 2 |
6 | 2, 5 | bd0r 10616 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wceq 1284 wss 2973 c0 3251 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-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-bd0 10604 ax-bdim 10605 ax-bdn 10608 ax-bdal 10609 ax-bdeq 10611 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-v 2603 df-dif 2975 df-in 2979 df-ss 2986 df-nul 3252 df-bdc 10632 |
This theorem is referenced by: bj-bd0el 10659 bj-nn0suc0 10745 |
Copyright terms: Public domain | W3C validator |