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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-sels | Unicode version |
Description: If a class is a set, then it is a member of a set. (Copied from set.mm.) (Contributed by BJ, 3-Apr-2019.) |
Ref | Expression |
---|---|
bj-sels |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snidg 3400 | . . 3 | |
2 | bj-snexg 10032 | . . . . 5 | |
3 | sbcel2g 2871 | . . . . 5 | |
4 | 2, 3 | syl 14 | . . . 4 |
5 | csbvarg 2877 | . . . . . 6 | |
6 | 2, 5 | syl 14 | . . . . 5 |
7 | 6 | eleq2d 2107 | . . . 4 |
8 | 4, 7 | bitrd 177 | . . 3 |
9 | 1, 8 | mpbird 156 | . 2 |
10 | 9 | spesbcd 2844 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wceq 1243 wex 1381 wcel 1393 cvv 2557 wsbc 2764 csb 2852 csn 3375 |
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-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-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-pr 3944 ax-bdor 9936 ax-bdeq 9940 ax-bdsep 10004 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-sbc 2765 df-csb 2853 df-un 2922 df-sn 3381 df-pr 3382 |
This theorem is referenced by: (None) |
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