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Mirrors > Home > ILE Home > Th. List > ss0b | Unicode version |
Description: Any subset of the empty set is empty. Theorem 5 of [Suppes] p. 23 and its converse. (Contributed by NM, 17-Sep-2003.) |
Ref | Expression |
---|---|
ss0b |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0ss 3406 | . . 3 | |
2 | eqss 3117 | . . 3 | |
3 | 1, 2 | mpbiran2 926 | . 2 |
4 | 3 | bicomi 131 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1332 wss 3076 c0 3368 |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-dif 3078 df-in 3082 df-ss 3089 df-nul 3369 |
This theorem is referenced by: ss0 3408 un00 3414 ssdisj 3424 pw0 3675 card0 7061 0nnei 12361 |
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