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Mirrors > Home > ILE Home > Th. List > 3onn | Unicode version |
Description: The ordinal 3 is a natural number. (Contributed by Mario Carneiro, 5-Jan-2016.) |
Ref | Expression |
---|---|
3onn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3o 6412 |
. 2
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2 | 2onn 6515 |
. . 3
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3 | peano2 4590 |
. . 3
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4 | 2, 3 | ax-mp 5 |
. 2
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5 | 1, 4 | eqeltri 2250 |
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-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-nul 4126 ax-pow 4171 ax-pr 4205 ax-un 4429 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-nul 3423 df-pw 3576 df-sn 3597 df-pr 3598 df-uni 3808 df-int 3843 df-suc 4367 df-iom 4586 df-1o 6410 df-2o 6411 df-3o 6412 |
This theorem is referenced by: 4onn 6517 hash4 10765 |
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