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 3422 | . 2 | |
2 | alnex 1486 | . 2 | |
3 | 1, 2 | bitr2i 184 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wb 104 wal 1340 wceq 1342 wex 1479 wcel 2135 c0 3404 |
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 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-dif 3113 df-nul 3405 |
This theorem is referenced by: disjnim 3967 pwntru 4172 exmidn0m 4174 mapprc 6609 map0g 6645 ixpprc 6676 ixp0 6688 exmidfodomrlemim 7148 ntreq0 12679 blssioo 13092 pwtrufal 13718 |
Copyright terms: Public domain | W3C validator |