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Mirrors > Home > ILE Home > Th. List > moop2 | Unicode version |
Description: "At most one" property of an ordered pair. (Contributed by NM, 11-Apr-2004.) (Revised by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
moop2.1 |
Ref | Expression |
---|---|
moop2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqtr2 2058 | . . . 4 | |
2 | moop2.1 | . . . . . 6 | |
3 | vex 2560 | . . . . . 6 | |
4 | 2, 3 | opth 3974 | . . . . 5 |
5 | 4 | simprbi 260 | . . . 4 |
6 | 1, 5 | syl 14 | . . 3 |
7 | 6 | gen2 1339 | . 2 |
8 | nfcsb1v 2882 | . . . . 5 | |
9 | nfcv 2178 | . . . . 5 | |
10 | 8, 9 | nfop 3565 | . . . 4 |
11 | 10 | nfeq2 2189 | . . 3 |
12 | csbeq1a 2860 | . . . . 5 | |
13 | id 19 | . . . . 5 | |
14 | 12, 13 | opeq12d 3557 | . . . 4 |
15 | 14 | eqeq2d 2051 | . . 3 |
16 | 11, 15 | mo4f 1960 | . 2 |
17 | 7, 16 | mpbir 134 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wal 1241 wceq 1243 wcel 1393 wmo 1901 cvv 2557 csb 2852 cop 3378 |
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 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 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-nfc 2167 df-v 2559 df-sbc 2765 df-csb 2853 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 |
This theorem is referenced by: (None) |
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