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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 |
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Ref | Expression |
---|---|
peano2zd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zred.1 |
. 2
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2 | peano2z 9287 |
. 2
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3 | 1, 2 | syl 14 |
1
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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 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4121 ax-pow 4174 ax-pr 4209 ax-setind 4536 ax-cnex 7901 ax-resscn 7902 ax-1cn 7903 ax-1re 7904 ax-icn 7905 ax-addcl 7906 ax-addrcl 7907 ax-mulcl 7908 ax-addcom 7910 ax-addass 7912 ax-distr 7914 ax-i2m1 7915 ax-0id 7918 ax-rnegex 7919 ax-cnre 7921 |
This theorem depends on definitions: df-bi 117 df-3or 979 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-reu 2462 df-rab 2464 df-v 2739 df-sbc 2963 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-int 3845 df-br 4004 df-opab 4065 df-id 4293 df-xp 4632 df-rel 4633 df-cnv 4634 df-co 4635 df-dm 4636 df-iota 5178 df-fun 5218 df-fv 5224 df-riota 5830 df-ov 5877 df-oprab 5878 df-mpo 5879 df-sub 8128 df-neg 8129 df-inn 8918 df-n0 9175 df-z 9252 |
This theorem is referenced by: elfzp1 10069 fznatpl1 10073 fzdifsuc 10078 fseq1p1m1 10091 flqge 10279 2tnp1ge0ge0 10298 ceiqm1l 10308 addmodlteq 10395 frec2uzzd 10397 frec2uzrdg 10406 uzsinds 10439 seq3f1olemqsumkj 10495 seq3f1olemqsumk 10496 bcp1nk 10737 bcval5 10738 hashfz 10796 resqrexlemdecn 11016 telfsumo 11469 fsumparts 11473 binomlem 11486 geo2sum 11517 cvgratnnlemseq 11529 cvgratnnlemabsle 11530 cvgratnnlemsumlt 11531 cvgratnnlemrate 11533 cvgratz 11535 mertenslemub 11537 mertenslemi1 11538 clim2prod 11542 clim2divap 11543 fprodntrivap 11587 fprodeq0 11620 dvdsfac 11860 2tp1odd 11883 opoe 11894 zsupcllemstep 11940 suprzubdc 11947 prmind2 12114 hashdvds 12215 eulerthlemrprm 12223 pcprendvds 12284 nninfdclemcl 12443 nninfdclemp1 12445 lgslem1 14294 lgsval 14298 lgsfvalg 14299 lgsval2lem 14304 lgsvalmod 14313 cvgcmp2nlemabs 14662 |
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