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Mirrors > Home > ILE Home > Th. List > abssexg | Unicode version |
Description: Existence of a class of subsets. (Contributed by NM, 15-Jul-2006.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
abssexg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pwexg 3933 | . 2 | |
2 | df-pw 3361 | . . . 4 | |
3 | 2 | eleq1i 2103 | . . 3 |
4 | simpl 102 | . . . . 5 | |
5 | 4 | ss2abi 3012 | . . . 4 |
6 | ssexg 3896 | . . . 4 | |
7 | 5, 6 | mpan 400 | . . 3 |
8 | 3, 7 | sylbi 114 | . 2 |
9 | 1, 8 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wcel 1393 cab 2026 cvv 2557 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 |
This theorem is referenced by: (None) |
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