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Mirrors > Home > ILE Home > Th. List > 8nn | Unicode version |
Description: 8 is a positive integer. (Contributed by Mario Carneiro, 15-Sep-2013.) |
Ref | Expression |
---|---|
8nn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-8 8695 |
. 2
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2 | 7nn 8790 |
. . 3
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3 | peano2nn 8642 |
. . 3
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4 | 2, 3 | ax-mp 7 |
. 2
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5 | 1, 4 | eqeltri 2187 |
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 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 ax-sep 4006 ax-cnex 7636 ax-resscn 7637 ax-1re 7639 ax-addrcl 7642 |
This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-ral 2395 df-rex 2396 df-v 2659 df-un 3041 df-in 3043 df-ss 3050 df-sn 3499 df-pr 3500 df-op 3502 df-uni 3703 df-int 3738 df-br 3896 df-iota 5046 df-fv 5089 df-ov 5731 df-inn 8631 df-2 8689 df-3 8690 df-4 8691 df-5 8692 df-6 8693 df-7 8694 df-8 8695 |
This theorem is referenced by: 9nn 8792 8nn0 8904 ipndx 11940 ipid 11941 ipslid 11942 ipsstrd 11943 |
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