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Mirrors > Home > ILE Home > Th. List > numnncl2 | Unicode version |
Description: Closure for a decimal integer (zero units place). (Contributed by Mario Carneiro, 9-Mar-2015.) |
Ref | Expression |
---|---|
numnncl2.1 |
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numnncl2.2 |
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Ref | Expression |
---|---|
numnncl2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | numnncl2.1 |
. . . . 5
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2 | numnncl2.2 |
. . . . 5
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3 | 1, 2 | nnmulcli 8542 |
. . . 4
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4 | 3 | nncni 8530 |
. . 3
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5 | 4 | addid1i 7721 |
. 2
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6 | 5, 3 | eqeltri 2167 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-sep 3978 ax-cnex 7533 ax-resscn 7534 ax-1cn 7535 ax-1re 7536 ax-icn 7537 ax-addcl 7538 ax-addrcl 7539 ax-mulcl 7540 ax-mulcom 7543 ax-addass 7544 ax-mulass 7545 ax-distr 7546 ax-1rid 7549 ax-0id 7550 ax-cnre 7553 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-nf 1402 df-sb 1700 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ral 2375 df-rex 2376 df-rab 2379 df-v 2635 df-un 3017 df-in 3019 df-ss 3026 df-sn 3472 df-pr 3473 df-op 3475 df-uni 3676 df-int 3711 df-br 3868 df-iota 5014 df-fv 5057 df-ov 5693 df-inn 8521 |
This theorem is referenced by: decnncl2 8999 |
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