Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ltp1d | Unicode version |
Description: A number is less than itself plus 1. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
ltp1d.1 |
Ref | Expression |
---|---|
ltp1d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltp1d.1 | . 2 | |
2 | ltp1 8730 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2135 class class class wbr 3976 (class class class)co 5836 cr 7743 c1 7745 caddc 7747 clt 7924 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-un 4405 ax-setind 4508 ax-cnex 7835 ax-resscn 7836 ax-1cn 7837 ax-1re 7838 ax-icn 7839 ax-addcl 7840 ax-addrcl 7841 ax-mulcl 7842 ax-addcom 7844 ax-addass 7846 ax-i2m1 7849 ax-0lt1 7850 ax-0id 7852 ax-rnegex 7853 ax-pre-ltadd 7860 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-nel 2430 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2723 df-dif 3113 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-xp 4604 df-iota 5147 df-fv 5190 df-ov 5839 df-pnf 7926 df-mnf 7927 df-ltxr 7929 |
This theorem is referenced by: zltp1le 9236 fznatpl1 10001 fzp1disj 10005 fzneuz 10026 fzp1nel 10029 fzonn0p1 10136 rebtwn2z 10180 seq3f1olemqsumk 10424 bernneq3 10566 bcp1nk 10664 bcpasc 10668 hashfzp1 10726 seq3coll 10741 resqrexlemover 10938 fsum1p 11345 cvgratnnlembern 11450 cvgratnnlemseq 11453 cvgratnnlemfm 11456 cvgratz 11459 mertenslemi1 11462 fprodntrivap 11511 fprod1p 11526 fprodeq0 11544 efcllemp 11585 nno 11828 zssinfcl 11866 sqrt2irr 12073 pcprendvds 12201 pcmpt 12252 exmidunben 12302 nninfdclemp1 12328 suplociccreex 13149 cvgcmp2nlemabs 13752 |
Copyright terms: Public domain | W3C validator |