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Mirrors > Home > ILE Home > Th. List > peano2zd | Unicode version |
Description: Deduction from second Peano postulate generalized to integers. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
zred.1 |
Ref | Expression |
---|---|
peano2zd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zred.1 | . 2 | |
2 | peano2z 9090 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 (class class class)co 5774 c1 7621 caddc 7623 cz 9054 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-setind 4452 ax-cnex 7711 ax-resscn 7712 ax-1cn 7713 ax-1re 7714 ax-icn 7715 ax-addcl 7716 ax-addrcl 7717 ax-mulcl 7718 ax-addcom 7720 ax-addass 7722 ax-distr 7724 ax-i2m1 7725 ax-0id 7728 ax-rnegex 7729 ax-cnre 7731 |
This theorem depends on definitions: df-bi 116 df-3or 963 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-ral 2421 df-rex 2422 df-reu 2423 df-rab 2425 df-v 2688 df-sbc 2910 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-int 3772 df-br 3930 df-opab 3990 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-iota 5088 df-fun 5125 df-fv 5131 df-riota 5730 df-ov 5777 df-oprab 5778 df-mpo 5779 df-sub 7935 df-neg 7936 df-inn 8721 df-n0 8978 df-z 9055 |
This theorem is referenced by: elfzp1 9852 fznatpl1 9856 fzdifsuc 9861 fseq1p1m1 9874 flqge 10055 2tnp1ge0ge0 10074 ceiqm1l 10084 addmodlteq 10171 frec2uzzd 10173 frec2uzrdg 10182 uzsinds 10215 seq3f1olemqsumkj 10271 seq3f1olemqsumk 10272 bcp1nk 10508 bcval5 10509 hashfz 10567 resqrexlemdecn 10784 telfsumo 11235 fsumparts 11239 binomlem 11252 geo2sum 11283 cvgratnnlemseq 11295 cvgratnnlemabsle 11296 cvgratnnlemsumlt 11297 cvgratnnlemrate 11299 cvgratz 11301 mertenslemub 11303 mertenslemi1 11304 clim2prod 11308 clim2divap 11309 dvdsfac 11558 2tp1odd 11581 opoe 11592 zsupcllemstep 11638 prmind2 11801 hashdvds 11897 cvgcmp2nlemabs 13227 |
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