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Mirrors > Home > ILE Home > Th. List > 4nn | Unicode version |
Description: 4 is a positive integer. (Contributed by NM, 8-Jan-2006.) |
Ref | Expression |
---|---|
4nn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-4 8581 |
. 2
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2 | 3nn 8676 |
. . 3
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3 | peano2nn 8532 |
. . 3
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4 | 2, 3 | ax-mp 7 |
. 2
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5 | 1, 4 | eqeltri 2167 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-sep 3978 ax-cnex 7533 ax-resscn 7534 ax-1re 7536 ax-addrcl 7539 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-nf 1402 df-sb 1700 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ral 2375 df-rex 2376 df-v 2635 df-un 3017 df-in 3019 df-ss 3026 df-sn 3472 df-pr 3473 df-op 3475 df-uni 3676 df-int 3711 df-br 3868 df-iota 5014 df-fv 5057 df-ov 5693 df-inn 8521 df-2 8579 df-3 8580 df-4 8581 |
This theorem is referenced by: 5nn 8678 4nn0 8790 4z 8878 fldiv4p1lem1div2 9861 iexpcyc 10190 resqrexlemnmsq 10581 ef01bndlem 11212 flodddiv4 11377 flodddiv4t2lthalf 11380 6lcm4e12 11512 starvndx 11778 starvid 11779 starvslid 11780 srngstrd 11781 |
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