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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 1945 | . . 3 | |
2 | 1 | albii 1463 | . 2 |
3 | nfv 1521 | . . 3 | |
4 | 3 | sb8 1849 | . 2 |
5 | eq0 3432 | . . 3 | |
6 | df-clab 2157 | . . . . 5 | |
7 | 6 | notbii 663 | . . . 4 |
8 | 7 | albii 1463 | . . 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 1346 wceq 1348 wsb 1755 wcel 2141 cab 2156 c0 3414 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-dif 3123 df-nul 3415 |
This theorem is referenced by: opprc 3784 |
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