New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > mob | Unicode version |
Description: Equality implied by "at most one." (Contributed by NM, 18-Feb-2006.) |
Ref | Expression |
---|---|
moi.1 | |
moi.2 |
Ref | Expression |
---|---|
mob |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2867 | . . . . 5 | |
2 | nfcv 2489 | . . . . . . . 8 | |
3 | nfv 1619 | . . . . . . . . . 10 | |
4 | nfmo1 2215 | . . . . . . . . . 10 | |
5 | nfv 1619 | . . . . . . . . . 10 | |
6 | 3, 4, 5 | nf3an 1827 | . . . . . . . . 9 |
7 | nfv 1619 | . . . . . . . . 9 | |
8 | 6, 7 | nfim 1813 | . . . . . . . 8 |
9 | moi.1 | . . . . . . . . . 10 | |
10 | 9 | 3anbi3d 1258 | . . . . . . . . 9 |
11 | eqeq1 2359 | . . . . . . . . . 10 | |
12 | 11 | bibi1d 310 | . . . . . . . . 9 |
13 | 10, 12 | imbi12d 311 | . . . . . . . 8 |
14 | moi.2 | . . . . . . . . 9 | |
15 | 14 | mob2 3016 | . . . . . . . 8 |
16 | 2, 8, 13, 15 | vtoclgf 2913 | . . . . . . 7 |
17 | 16 | com12 27 | . . . . . 6 |
18 | 17 | 3expib 1154 | . . . . 5 |
19 | 1, 18 | syl 15 | . . . 4 |
20 | 19 | com3r 73 | . . 3 |
21 | 20 | imp 418 | . 2 |
22 | 21 | 3impib 1149 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 w3a 934 wceq 1642 wcel 1710 wmo 2205 cvv 2859 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-mo 2209 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 |
This theorem is referenced by: moi 3019 rmob 3134 |
Copyright terms: Public domain | W3C validator |