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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 8976 |
. . . 4
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4 | 3 | nncni 8964 |
. . 3
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5 | 4 | addid1i 8134 |
. 2
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6 | 5, 3 | eqeltri 2262 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-sep 4139 ax-cnex 7937 ax-resscn 7938 ax-1cn 7939 ax-1re 7940 ax-icn 7941 ax-addcl 7942 ax-addrcl 7943 ax-mulcl 7944 ax-mulcom 7947 ax-addass 7948 ax-mulass 7949 ax-distr 7950 ax-1rid 7953 ax-0id 7954 ax-cnre 7957 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3616 df-pr 3617 df-op 3619 df-uni 3828 df-int 3863 df-br 4022 df-iota 5199 df-fv 5246 df-ov 5903 df-inn 8955 |
This theorem is referenced by: decnncl2 9442 |
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