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| 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 8917 |
. 2
| |
| 3 | 1, 2 | syl 14 |
1
|
| 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 615 ax-in2 616 ax-io 711 ax-5 1470 ax-7 1471 ax-gen 1472 ax-ie1 1516 ax-ie2 1517 ax-8 1527 ax-10 1528 ax-11 1529 ax-i12 1530 ax-bndl 1532 ax-4 1533 ax-17 1549 ax-i9 1553 ax-ial 1557 ax-i5r 1558 ax-13 2178 ax-14 2179 ax-ext 2187 ax-sep 4162 ax-pow 4218 ax-pr 4253 ax-un 4480 ax-setind 4585 ax-cnex 8016 ax-resscn 8017 ax-1cn 8018 ax-1re 8019 ax-icn 8020 ax-addcl 8021 ax-addrcl 8022 ax-mulcl 8023 ax-addcom 8025 ax-addass 8027 ax-i2m1 8030 ax-0lt1 8031 ax-0id 8033 ax-rnegex 8034 ax-pre-ltadd 8041 |
| This theorem depends on definitions: df-bi 117 df-3an 983 df-tru 1376 df-fal 1379 df-nf 1484 df-sb 1786 df-eu 2057 df-mo 2058 df-clab 2192 df-cleq 2198 df-clel 2201 df-nfc 2337 df-ne 2377 df-nel 2472 df-ral 2489 df-rex 2490 df-rab 2493 df-v 2774 df-dif 3168 df-un 3170 df-in 3172 df-ss 3179 df-pw 3618 df-sn 3639 df-pr 3640 df-op 3642 df-uni 3851 df-br 4045 df-opab 4106 df-xp 4681 df-iota 5232 df-fv 5279 df-ov 5947 df-pnf 8109 df-mnf 8110 df-ltxr 8112 |
| This theorem is referenced by: zltp1le 9427 fznatpl1 10198 fzp1disj 10202 fzneuz 10223 fzp1nel 10226 fzonn0p1 10340 zssinfcl 10375 rebtwn2z 10397 seq3f1olemqsumk 10657 seqf1oglem1 10664 seqf1oglem2 10665 bernneq3 10807 bcp1nk 10907 bcpasc 10911 hashfzp1 10969 seq3coll 10987 resqrexlemover 11321 fsum1p 11729 cvgratnnlembern 11834 cvgratnnlemseq 11837 cvgratnnlemfm 11840 cvgratz 11843 mertenslemi1 11846 fprodntrivap 11895 fprod1p 11910 fprodeq0 11928 efcllemp 11969 nno 12217 sqrt2irr 12484 pcprendvds 12613 pcmpt 12666 1arith 12690 4sqlem11 12724 exmidunben 12797 nninfdclemp1 12821 suplociccreex 15096 perfectlem2 15472 gausslemma2dlem4 15541 gausslemma2dlem6 15544 lgsquadlem2 15555 cvgcmp2nlemabs 15971 |
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