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Mirrors > Home > ILE Home > Th. List > nn0pnfge0 | Unicode version |
Description: If a number is a nonnegative integer or positive infinity, it is greater than or equal to 0. (Contributed by Alexander van der Vekens, 6-Jan-2018.) |
Ref | Expression |
---|---|
nn0pnfge0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0ge0 9220 |
. 2
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2 | 0lepnf 9809 |
. . 3
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3 | breq2 4022 |
. . 3
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4 | 2, 3 | mpbiri 168 |
. 2
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5 | 1, 4 | jaoi 717 |
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-in1 615 ax-in2 616 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-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4189 ax-pr 4224 ax-un 4448 ax-setind 4551 ax-cnex 7921 ax-resscn 7922 ax-1cn 7923 ax-1re 7924 ax-icn 7925 ax-addcl 7926 ax-addrcl 7927 ax-mulcl 7928 ax-i2m1 7935 ax-0lt1 7936 ax-0id 7938 ax-rnegex 7939 ax-pre-ltirr 7942 ax-pre-ltwlin 7943 ax-pre-lttrn 7944 ax-pre-ltadd 7946 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-nel 2456 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-int 3860 df-br 4019 df-opab 4080 df-xp 4647 df-cnv 4649 df-iota 5193 df-fv 5239 df-ov 5894 df-pnf 8013 df-mnf 8014 df-xr 8015 df-ltxr 8016 df-le 8017 df-inn 8939 df-n0 9196 |
This theorem is referenced by: (None) |
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