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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 4645 | . . 3 | |
2 | 1 | con3i 627 | . 2 |
3 | df-res 4623 | . . . 4 | |
4 | incom 3319 | . . . 4 | |
5 | 3, 4 | eqtri 2191 | . . 3 |
6 | disjsn 3645 | . . . 4 | |
7 | 6 | biimpri 132 | . . 3 |
8 | 5, 7 | eqtrid 2215 | . 2 |
9 | 2, 8 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1348 wcel 2141 cvv 2730 cin 3120 c0 3414 csn 3583 cop 3586 cxp 4609 cres 4613 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-nul 3415 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-opab 4051 df-xp 4617 df-res 4623 |
This theorem is referenced by: fvunsng 5690 fsnunres 5698 |
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