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Mirrors > Home > ILE Home > Th. List > nnrpd | Unicode version |
Description: A positive integer is a positive real. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
nnrpd.1 |
Ref | Expression |
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nnrpd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnrpd.1 | . 2 | |
2 | nnrp 8743 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1433 cn 8039 crp 8734 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 ax-un 4188 ax-setind 4280 ax-cnex 7067 ax-resscn 7068 ax-1re 7070 ax-addrcl 7073 ax-0lt1 7082 ax-0id 7084 ax-rnegex 7085 ax-pre-ltirr 7088 ax-pre-ltwlin 7089 ax-pre-lttrn 7090 ax-pre-ltadd 7092 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ne 2246 df-nel 2340 df-ral 2353 df-rex 2354 df-rab 2357 df-v 2603 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-int 3637 df-br 3786 df-opab 3840 df-xp 4369 df-cnv 4371 df-iota 4887 df-fv 4930 df-ov 5535 df-pnf 7155 df-mnf 7156 df-xr 7157 df-ltxr 7158 df-le 7159 df-inn 8040 df-rp 8735 |
This theorem is referenced by: qtri3or 9252 qbtwnrelemcalc 9264 qbtwnre 9265 flqdiv 9323 addmodlteq 9400 nnesq 9592 bcpasc 9693 cvg1nlemcxze 9868 cvg1nlemcau 9870 cvg1nlemres 9871 resqrexlemnmsq 9903 resqrexlemnm 9904 resqrexlemcvg 9905 climrecvg1n 10185 climcvg1nlem 10186 prmind2 10502 sqrt2irrlem 10540 sqrt2irraplemnn 10557 sqrt2irrap 10558 |
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