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Mirrors > Home > ILE Home > Th. List > reusv1 | Unicode version |
Description: Two ways to express single-valuedness of a class expression . (Contributed by NM, 16-Dec-2012.) (Proof shortened by Mario Carneiro, 18-Nov-2016.) |
Ref | Expression |
---|---|
reusv1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfra1 2355 | . . . 4 | |
2 | 1 | nfmo 1920 | . . 3 |
3 | rsp 2369 | . . . . . . . 8 | |
4 | 3 | impd 242 | . . . . . . 7 |
5 | 4 | com12 27 | . . . . . 6 |
6 | 5 | alrimiv 1754 | . . . . 5 |
7 | moeq 2716 | . . . . 5 | |
8 | moim 1964 | . . . . 5 | |
9 | 6, 7, 8 | mpisyl 1335 | . . . 4 |
10 | 9 | ex 108 | . . 3 |
11 | 2, 10 | rexlimi 2426 | . 2 |
12 | mormo 2521 | . 2 | |
13 | reu5 2522 | . . 3 | |
14 | 13 | rbaib 830 | . 2 |
15 | 11, 12, 14 | 3syl 17 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wcel 1393 wmo 1901 wral 2306 wrex 2307 wreu 2308 wrmo 2309 |
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-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-ral 2311 df-rex 2312 df-reu 2313 df-rmo 2314 df-v 2559 |
This theorem is referenced by: (None) |
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