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Mirrors > Home > ILE Home > Th. List > sbeqalb | Unicode version |
Description: Theorem *14.121 in [WhiteheadRussell] p. 185. (Contributed by Andrew Salmon, 28-Jun-2011.) (Proof shortened by Wolf Lammen, 9-May-2013.) |
Ref | Expression |
---|---|
sbeqalb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bibi1 229 | . . . . 5 | |
2 | 1 | biimpa 280 | . . . 4 |
3 | 2 | biimpd 132 | . . 3 |
4 | 3 | alanimi 1348 | . 2 |
5 | sbceqal 2814 | . 2 | |
6 | 4, 5 | syl5 28 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wcel 1393 |
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: iotaval 4878 |
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