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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 2189 | . . . 4 | |
2 | moop2.1 | . . . . . 6 | |
3 | vex 2733 | . . . . . 6 | |
4 | 2, 3 | opth 4222 | . . . . 5 |
5 | 4 | simprbi 273 | . . . 4 |
6 | 1, 5 | syl 14 | . . 3 |
7 | 6 | gen2 1443 | . 2 |
8 | nfcsb1v 3082 | . . . . 5 | |
9 | nfcv 2312 | . . . . 5 | |
10 | 8, 9 | nfop 3781 | . . . 4 |
11 | 10 | nfeq2 2324 | . . 3 |
12 | csbeq1a 3058 | . . . . 5 | |
13 | id 19 | . . . . 5 | |
14 | 12, 13 | opeq12d 3773 | . . . 4 |
15 | 14 | eqeq2d 2182 | . . 3 |
16 | 11, 15 | mo4f 2079 | . 2 |
17 | 7, 16 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1346 wceq 1348 wmo 2020 wcel 2141 cvv 2730 csb 3049 cop 3586 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-sbc 2956 df-csb 3050 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 |
This theorem is referenced by: (None) |
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