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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 9058 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1465 (class class class)co 5742 c1 7589 caddc 7591 cz 9022 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-setind 4422 ax-cnex 7679 ax-resscn 7680 ax-1cn 7681 ax-1re 7682 ax-icn 7683 ax-addcl 7684 ax-addrcl 7685 ax-mulcl 7686 ax-addcom 7688 ax-addass 7690 ax-distr 7692 ax-i2m1 7693 ax-0id 7696 ax-rnegex 7697 ax-cnre 7699 |
This theorem depends on definitions: df-bi 116 df-3or 948 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-ral 2398 df-rex 2399 df-reu 2400 df-rab 2402 df-v 2662 df-sbc 2883 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-int 3742 df-br 3900 df-opab 3960 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-iota 5058 df-fun 5095 df-fv 5101 df-riota 5698 df-ov 5745 df-oprab 5746 df-mpo 5747 df-sub 7903 df-neg 7904 df-inn 8689 df-n0 8946 df-z 9023 |
This theorem is referenced by: elfzp1 9820 fznatpl1 9824 fzdifsuc 9829 fseq1p1m1 9842 flqge 10023 2tnp1ge0ge0 10042 ceiqm1l 10052 addmodlteq 10139 frec2uzzd 10141 frec2uzrdg 10150 uzsinds 10183 seq3f1olemqsumkj 10239 seq3f1olemqsumk 10240 bcp1nk 10476 bcval5 10477 hashfz 10535 resqrexlemdecn 10752 telfsumo 11203 fsumparts 11207 binomlem 11220 geo2sum 11251 cvgratnnlemseq 11263 cvgratnnlemabsle 11264 cvgratnnlemsumlt 11265 cvgratnnlemrate 11267 cvgratz 11269 mertenslemub 11271 mertenslemi1 11272 dvdsfac 11485 2tp1odd 11508 opoe 11519 zsupcllemstep 11565 prmind2 11728 hashdvds 11824 cvgcmp2nlemabs 13154 |
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