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Mirrors > Home > ILE Home > Th. List > decnncl2 | Unicode version |
Description: Closure for a decimal integer (zero units place). (Contributed by Mario Carneiro, 17-Apr-2015.) (Revised by AV, 6-Sep-2021.) |
Ref | Expression |
---|---|
decnncl2.1 |
Ref | Expression |
---|---|
decnncl2 | ; |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfdec10 9333 | . 2 ; ; | |
2 | 10nn 9345 | . . 3 ; | |
3 | decnncl2.1 | . . 3 | |
4 | 2, 3 | numnncl2 9352 | . 2 ; |
5 | 1, 4 | eqeltri 2243 | 1 ; |
Colors of variables: wff set class |
Syntax hints: wcel 2141 (class class class)co 5850 cc0 7761 c1 7762 caddc 7764 cmul 7766 cn 8865 ;cdc 9330 |
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-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-ext 2152 ax-sep 4105 ax-cnex 7852 ax-resscn 7853 ax-1cn 7854 ax-1re 7855 ax-icn 7856 ax-addcl 7857 ax-addrcl 7858 ax-mulcl 7859 ax-mulcom 7862 ax-addass 7863 ax-mulass 7864 ax-distr 7865 ax-1rid 7868 ax-0id 7869 ax-cnre 7872 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 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-rab 2457 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-int 3830 df-br 3988 df-iota 5158 df-fv 5204 df-ov 5853 df-inn 8866 df-2 8924 df-3 8925 df-4 8926 df-5 8927 df-6 8928 df-7 8929 df-8 8930 df-9 8931 df-dec 9331 |
This theorem is referenced by: 3dec 10635 |
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