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Mirrors > Home > ILE Home > Th. List > nlim0 | Unicode version |
Description: The empty set is not a limit ordinal. (Contributed by NM, 24-Mar-1995.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
nlim0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3409 | . . 3 | |
2 | simp2 987 | . . 3 | |
3 | 1, 2 | mto 652 | . 2 |
4 | dflim2 4343 | . 2 | |
5 | 3, 4 | mtbir 661 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 w3a 967 wceq 1342 wcel 2135 c0 3405 cuni 3784 word 4335 wlim 4337 |
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-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2724 df-dif 3114 df-nul 3406 df-ilim 4342 |
This theorem is referenced by: (None) |
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