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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 2397 | . . . 4 | |
2 | 1 | nfmo 1961 | . . 3 |
3 | rsp 2411 | . . . . . . . 8 | |
4 | 3 | impd 251 | . . . . . . 7 |
5 | 4 | com12 30 | . . . . . 6 |
6 | 5 | alrimiv 1795 | . . . . 5 |
7 | moeq 2767 | . . . . 5 | |
8 | moim 2005 | . . . . 5 | |
9 | 6, 7, 8 | mpisyl 1375 | . . . 4 |
10 | 9 | ex 113 | . . 3 |
11 | 2, 10 | rexlimi 2470 | . 2 |
12 | mormo 2565 | . 2 | |
13 | reu5 2566 | . . 3 | |
14 | 13 | rbaib 863 | . 2 |
15 | 11, 12, 14 | 3syl 17 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wceq 1284 wcel 1433 wmo 1942 wral 2348 wrex 2349 wreu 2350 wrmo 2351 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-ral 2353 df-rex 2354 df-reu 2355 df-rmo 2356 df-v 2603 |
This theorem is referenced by: (None) |
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