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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 2488 | . . . 4 | |
2 | 1 | nfmo 2026 | . . 3 |
3 | rsp 2504 | . . . . . . . 8 | |
4 | 3 | impd 252 | . . . . . . 7 |
5 | 4 | com12 30 | . . . . . 6 |
6 | 5 | alrimiv 1854 | . . . . 5 |
7 | moeq 2887 | . . . . 5 | |
8 | moim 2070 | . . . . 5 | |
9 | 6, 7, 8 | mpisyl 1426 | . . . 4 |
10 | 9 | ex 114 | . . 3 |
11 | 2, 10 | rexlimi 2567 | . 2 |
12 | mormo 2668 | . 2 | |
13 | reu5 2669 | . . 3 | |
14 | 13 | rbaib 907 | . 2 |
15 | 11, 12, 14 | 3syl 17 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1333 wceq 1335 wmo 2007 wcel 2128 wral 2435 wrex 2436 wreu 2437 wrmo 2438 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-ral 2440 df-rex 2441 df-reu 2442 df-rmo 2443 df-v 2714 |
This theorem is referenced by: (None) |
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