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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2255 |
. . 3
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2 | nfcv 2255 |
. . 3
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3 | 1, 2 | cleqf 2279 |
. 2
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4 | noel 3333 |
. . . 4
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5 | 4 | nbn 671 |
. . 3
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6 | 5 | albii 1429 |
. 2
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7 | 3, 6 | bitr4i 186 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 586 ax-in2 587 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-v 2659 df-dif 3039 df-nul 3330 |
This theorem is referenced by: notm0 3349 nel0 3350 0el 3351 rabeq0 3358 abeq0 3359 ssdif0im 3393 inssdif0im 3396 ralf0 3432 snprc 3554 uni0b 3727 disjiun 3890 0ex 4015 dm0 4713 reldm0 4717 dmsn0 4964 dmsn0el 4966 fzo0 9838 fzouzdisj 9850 |
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