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Mirrors > Home > ILE Home > Th. List > eq0 | Unicode version |
Description: The empty set has no elements. Theorem 2 of [Suppes] p. 22. (Contributed by NM, 29-Aug-1993.) |
Ref | Expression |
---|---|
eq0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2281 | . . 3 | |
2 | nfcv 2281 | . . 3 | |
3 | 1, 2 | cleqf 2305 | . 2 |
4 | noel 3367 | . . . 4 | |
5 | 4 | nbn 688 | . . 3 |
6 | 5 | albii 1446 | . 2 |
7 | 3, 6 | bitr4i 186 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wb 104 wal 1329 wceq 1331 wcel 1480 c0 3363 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-dif 3073 df-nul 3364 |
This theorem is referenced by: notm0 3383 nel0 3384 0el 3385 rabeq0 3392 abeq0 3393 ssdif0im 3427 inssdif0im 3430 ralf0 3466 snprc 3588 uni0b 3761 disjiun 3924 0ex 4055 dm0 4753 reldm0 4757 dmsn0 5006 dmsn0el 5008 fzo0 9945 fzouzdisj 9957 |
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