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Mirrors > Home > ILE Home > Th. List > abeq0 | Unicode version |
Description: Condition for a class abstraction to be empty. (Contributed by Jim Kingdon, 12-Aug-2018.) |
Ref | Expression |
---|---|
abeq0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbn 1903 | . . 3 | |
2 | 1 | albii 1431 | . 2 |
3 | nfv 1493 | . . 3 | |
4 | 3 | sb8 1812 | . 2 |
5 | eq0 3351 | . . 3 | |
6 | df-clab 2104 | . . . . 5 | |
7 | 6 | notbii 642 | . . . 4 |
8 | 7 | albii 1431 | . . 3 |
9 | 5, 8 | bitri 183 | . 2 |
10 | 2, 4, 9 | 3bitr4ri 212 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wb 104 wal 1314 wceq 1316 wcel 1465 wsb 1720 cab 2103 c0 3333 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-dif 3043 df-nul 3334 |
This theorem is referenced by: opprc 3696 |
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