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Mirrors > Home > ILE Home > Th. List > ressnop0 | Unicode version |
Description: If is not in , then the restriction of a singleton of to is null. (Contributed by Scott Fenton, 15-Apr-2011.) |
Ref | Expression |
---|---|
ressnop0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelxp1 4619 | . . 3 | |
2 | 1 | con3i 622 | . 2 |
3 | df-res 4597 | . . . 4 | |
4 | incom 3299 | . . . 4 | |
5 | 3, 4 | eqtri 2178 | . . 3 |
6 | disjsn 3621 | . . . 4 | |
7 | 6 | biimpri 132 | . . 3 |
8 | 5, 7 | syl5eq 2202 | . 2 |
9 | 2, 8 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1335 wcel 2128 cvv 2712 cin 3101 c0 3394 csn 3560 cop 3563 cxp 4583 cres 4587 |
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-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3395 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-opab 4026 df-xp 4591 df-res 4597 |
This theorem is referenced by: fvunsng 5660 fsnunres 5668 |
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