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Mirrors > Home > ILE Home > Th. List > 6nn | Unicode version |
Description: 6 is a positive integer. (Contributed by Mario Carneiro, 15-Sep-2013.) |
Ref | Expression |
---|---|
6nn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-6 9013 |
. 2
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2 | 5nn 9114 |
. . 3
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3 | peano2nn 8962 |
. . 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 7933 ax-resscn 7934 ax-1re 7936 ax-addrcl 7939 |
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 5900 df-inn 8951 df-2 9009 df-3 9010 df-4 9011 df-5 9012 df-6 9013 |
This theorem is referenced by: 7nn 9116 6nn0 9228 ef01bndlem 11799 sin01bnd 11800 cos01bnd 11801 6gcd4e2 12031 6lcm4e12 12122 vscandx 12671 vscaid 12672 vscaslid 12677 lmodstrd 12678 ipsstrd 12690 psrvalstrd 13963 sincos3rdpi 14741 pigt3 14742 ex-dvds 14960 ex-gcd 14961 |
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