Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > notm0 | Unicode version |
Description: A class is not inhabited if and only if it is empty. (Contributed by Jim Kingdon, 1-Jul-2022.) |
Ref | Expression |
---|---|
notm0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eq0 3376 | . 2 | |
2 | alnex 1475 | . 2 | |
3 | 1, 2 | bitr2i 184 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wb 104 wal 1329 wceq 1331 wex 1468 wcel 1480 c0 3358 |
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-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-dif 3068 df-nul 3359 |
This theorem is referenced by: disjnim 3915 pwntru 4117 exmidn0m 4119 mapprc 6539 map0g 6575 ixpprc 6606 ixp0 6618 exmidfodomrlemim 7050 ntreq0 12290 blssioo 12703 pwtrufal 13181 |
Copyright terms: Public domain | W3C validator |