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Mirrors > Home > ILE Home > Th. List > sbceqal | Unicode version |
Description: A variation of extensionality for classes. (Contributed by Andrew Salmon, 28-Jun-2011.) |
Ref | Expression |
---|---|
sbceqal |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | spsbc 2775 | . 2 | |
2 | sbcimg 2804 | . . 3 | |
3 | eqid 2040 | . . . . 5 | |
4 | eqsbc3 2802 | . . . . 5 | |
5 | 3, 4 | mpbiri 157 | . . . 4 |
6 | pm5.5 231 | . . . 4 | |
7 | 5, 6 | syl 14 | . . 3 |
8 | eqsbc3 2802 | . . 3 | |
9 | 2, 7, 8 | 3bitrd 203 | . 2 |
10 | 1, 9 | sylibd 138 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wal 1241 wceq 1243 wcel 1393 wsbc 2764 |
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-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
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-sbc 2765 |
This theorem is referenced by: sbeqalb 2815 snsssn 3532 |
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