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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ss0b 3433 | . 2 | |
2 | 1 | biimpi 119 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 wss 3102 c0 3394 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-dif 3104 df-in 3108 df-ss 3115 df-nul 3395 |
This theorem is referenced by: sseq0 3435 abf 3437 eq0rdv 3438 ssdisj 3450 0dif 3465 poirr2 4978 iotanul 5150 f00 5361 map0b 6632 phplem2 6798 php5dom 6808 sbthlem7 6907 fi0 6919 casefun 7029 caseinj 7033 djufun 7048 djuinj 7050 nnnninfeq 7071 exmidomni 7085 ixxdisj 9807 icodisj 9896 ioodisj 9897 uzdisj 9995 nn0disj 10037 fsum2dlemstep 11331 fprodssdc 11487 fprod2dlemstep 11519 ntrcls0 12531 |
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