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Mirrors > Home > ILE Home > Th. List > 3nn0 | Unicode version |
Description: 3 is a nonnegative integer. (Contributed by Mario Carneiro, 18-Feb-2014.) |
Ref | Expression |
---|---|
3nn0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3nn 8906 |
. 2
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2 | 1 | nnnn0i 9009 |
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 df-3 8804 df-n0 9002 |
This theorem is referenced by: 7p4e11 9281 7p7e14 9284 8p4e12 9287 8p6e14 9289 9p4e13 9294 9p5e14 9295 4t4e16 9304 5t4e20 9307 6t4e24 9311 6t6e36 9313 7t4e28 9316 7t6e42 9318 8t4e32 9322 8t5e40 9323 9t4e36 9329 9t5e45 9330 9t7e63 9332 9t8e72 9333 4fvwrd4 9948 fldiv4p1lem1div2 10109 expnass 10429 binom3 10440 fac4 10511 4bc2eq6 10552 ef4p 11437 efi4p 11460 resin4p 11461 recos4p 11462 ef01bndlem 11499 sin01bnd 11500 sin01gt0 11504 tangtx 12967 |
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