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Mirrors > Home > ILE Home > Th. List > 9nn | Unicode version |
Description: 9 is a positive integer. (Contributed by NM, 21-Oct-2012.) |
Ref | Expression |
---|---|
9nn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-9 8944 | . 2 | |
2 | 8nn 9045 | . . 3 | |
3 | peano2nn 8890 | . . 3 | |
4 | 2, 3 | ax-mp 5 | . 2 |
5 | 1, 4 | eqeltri 2243 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2141 (class class class)co 5853 c1 7775 caddc 7777 cn 8878 c8 8935 c9 8936 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 ax-sep 4107 ax-cnex 7865 ax-resscn 7866 ax-1re 7868 ax-addrcl 7871 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-int 3832 df-br 3990 df-iota 5160 df-fv 5206 df-ov 5856 df-inn 8879 df-2 8937 df-3 8938 df-4 8939 df-5 8940 df-6 8941 df-7 8942 df-8 8943 df-9 8944 |
This theorem is referenced by: 9nn0 9159 9p1e10 9345 10nn 9358 3dvdsdec 11824 tsetndx 12566 tsetid 12567 tsetslid 12568 topgrpstrd 12569 eltpsg 12832 setsmsbasg 13273 2logb9irr 13683 sqrt2cxp2logb9e3 13687 2logb9irrap 13689 ex-gcd 13766 |
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