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Mirrors > Home > ILE Home > Th. List > 2nn | Unicode version |
Description: 2 is a positive integer. (Contributed by NM, 20-Aug-2001.) |
Ref | Expression |
---|---|
2nn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 8803 |
. 2
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2 | 1nn 8755 |
. . 3
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3 | peano2nn 8756 |
. . 3
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4 | 2, 3 | ax-mp 5 |
. 2
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5 | 1, 4 | eqeltri 2213 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-cnex 7735 ax-resscn 7736 ax-1re 7738 ax-addrcl 7741 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-int 3780 df-br 3938 df-iota 5096 df-fv 5139 df-ov 5785 df-inn 8745 df-2 8803 |
This theorem is referenced by: 3nn 8906 2nn0 9018 2z 9106 uz3m2nn 9395 ige2m1fz1 9920 qbtwnre 10065 flhalf 10106 sqeq0 10387 sqeq0d 10454 facavg 10524 bcn2 10542 resqrexlemnm 10822 abs00ap 10866 geo2sum 11315 geo2lim 11317 ege2le3 11414 ef01bndlem 11499 mod2eq0even 11611 mod2eq1n2dvds 11612 sqgcd 11753 3lcm2e6woprm 11803 prm2orodd 11843 3prm 11845 4nprm 11846 divgcdodd 11857 isevengcd2 11872 3lcm2e6 11874 pw2dvdslemn 11879 pw2dvds 11880 pw2dvdseulemle 11881 oddpwdclemxy 11883 oddpwdclemodd 11886 oddpwdclemdc 11887 oddpwdc 11888 sqpweven 11889 2sqpwodd 11890 evenennn 11942 exmidunben 11975 plusgndx 12091 plusgid 12092 plusgslid 12093 grpstrg 12105 grpbaseg 12106 grpplusgg 12107 rngstrg 12113 lmodstrd 12131 topgrpstrd 12149 dsndx 12156 dsid 12157 dsslid 12158 dveflem 12895 ex-fl 13108 ex-ceil 13109 redcwlpolemeq1 13421 |
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