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 9985 | . . 3 BOUNDED | |
2 | 1 | bdss 9984 | . 2 BOUNDED |
3 | 0ss 3255 | . . 3 | |
4 | eqss 2960 | . . 3 | |
5 | 3, 4 | mpbiran2 848 | . 2 |
6 | 2, 5 | bd0r 9945 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wceq 1243 wss 2917 c0 3224 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-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-bd0 9933 ax-bdim 9934 ax-bdn 9937 ax-bdal 9938 ax-bdeq 9940 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-v 2559 df-dif 2920 df-in 2924 df-ss 2931 df-nul 3225 df-bdc 9961 |
This theorem is referenced by: bj-bd0el 9988 bj-nn0suc0 10075 |
Copyright terms: Public domain | W3C validator |