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Mirrors > Home > ILE Home > Th. List > 5nn | Unicode version |
Description: 5 is a positive integer. (Contributed by Mario Carneiro, 15-Sep-2013.) |
Ref | Expression |
---|---|
5nn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-5 9011 |
. 2
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2 | 4nn 9112 |
. . 3
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3 | peano2nn 8961 |
. . 3
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4 | 2, 3 | ax-mp 5 |
. 2
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5 | 1, 4 | 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 4136 ax-cnex 7932 ax-resscn 7933 ax-1re 7935 ax-addrcl 7938 |
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-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-int 3860 df-br 4019 df-iota 5196 df-fv 5243 df-ov 5899 df-inn 8950 df-2 9008 df-3 9009 df-4 9010 df-5 9011 |
This theorem is referenced by: 6nn 9114 5nn0 9226 prm23ge5 12296 scandx 12662 scaid 12663 scaslid 12664 lmodstrd 12675 ipsstrd 12687 ccoid 12742 ccoslid 12743 psrvalstrd 13946 lgsdir2lem1 14887 lgsdir2lem3 14889 |
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