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Mirrors > Home > ILE Home > Th. List > ss0 | Unicode version |
Description: Any subset of the empty set is empty. Theorem 5 of [Suppes] p. 23. (Contributed by NM, 13-Aug-1994.) |
Ref | Expression |
---|---|
ss0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ss0b 3256 |
. 2
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2 | 1 | biimpi 113 |
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 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-dif 2920 df-in 2924 df-ss 2931 df-nul 3225 |
This theorem is referenced by: sseq0 3258 abf 3260 eq0rdv 3261 ssdisj 3277 disjpss 3278 0dif 3295 poirr2 4717 iotanul 4882 f00 5081 phplem2 6316 php5dom 6325 ixxdisj 8772 icodisj 8860 ioodisj 8861 uzdisj 8955 nn0disj 8995 |
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