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Mirrors > Home > ILE Home > Th. List > ssextss | Unicode version |
Description: An extensionality-like principle defining subclass in terms of subsets. (Contributed by NM, 30-Jun-2004.) |
Ref | Expression |
---|---|
ssextss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sspwb 3952 | . 2 | |
2 | dfss2 2934 | . 2 | |
3 | vex 2560 | . . . . 5 | |
4 | 3 | elpw 3365 | . . . 4 |
5 | 3 | elpw 3365 | . . . 4 |
6 | 4, 5 | imbi12i 228 | . . 3 |
7 | 6 | albii 1359 | . 2 |
8 | 1, 2, 7 | 3bitri 195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wal 1241 wcel 1393 wss 2917 cpw 3359 |
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-sep 3875 ax-pow 3927 |
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-v 2559 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 |
This theorem is referenced by: ssext 3957 nssssr 3958 |
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