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Mirrors > Home > MPE Home > Th. List > moop2 | Structured version Visualization version 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 2642 | . . . 4 | |
2 | moop2.1 | . . . . . 6 | |
3 | vex 3203 | . . . . . 6 | |
4 | 2, 3 | opth 4945 | . . . . 5 |
5 | 4 | simprbi 480 | . . . 4 |
6 | 1, 5 | syl 17 | . . 3 |
7 | 6 | gen2 1723 | . 2 |
8 | nfcsb1v 3549 | . . . . 5 | |
9 | nfcv 2764 | . . . . 5 | |
10 | 8, 9 | nfop 4418 | . . . 4 |
11 | 10 | nfeq2 2780 | . . 3 |
12 | csbeq1a 3542 | . . . . 5 | |
13 | id 22 | . . . . 5 | |
14 | 12, 13 | opeq12d 4410 | . . . 4 |
15 | 14 | eqeq2d 2632 | . . 3 |
16 | 11, 15 | mo4f 2516 | . 2 |
17 | 7, 16 | mpbir 221 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wal 1481 wceq 1483 wcel 1990 wmo 2471 cvv 3200 csb 3533 cop 4183 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 |
This theorem is referenced by: euop2 4974 |
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