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Mirrors > Home > MPE Home > Th. List > 1e0p1 | Structured version Visualization version Unicode version |
Description: The successor of zero. (Contributed by Mario Carneiro, 18-Feb-2014.) |
Ref | Expression |
---|---|
1e0p1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0p1e1 11132 | . 2 | |
2 | 1 | eqcomi 2631 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 (class class class)co 6650 cc0 9936 c1 9937 caddc 9939 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 ax-resscn 9993 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-addrcl 9997 ax-mulcl 9998 ax-mulrcl 9999 ax-mulcom 10000 ax-addass 10001 ax-mulass 10002 ax-distr 10003 ax-i2m1 10004 ax-1ne0 10005 ax-1rid 10006 ax-rnegex 10007 ax-rrecex 10008 ax-cnre 10009 ax-pre-lttri 10010 ax-pre-lttrn 10011 ax-pre-ltadd 10012 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-nel 2898 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-po 5035 df-so 5036 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-ov 6653 df-er 7742 df-en 7956 df-dom 7957 df-sdom 7958 df-pnf 10076 df-mnf 10077 df-ltxr 10079 |
This theorem is referenced by: 6p5e11 11600 6p5e11OLD 11601 7p4e11 11605 7p4e11OLD 11606 8p3e11 11612 8p3e11OLD 11613 9p2e11 11619 9p2e11OLD 11620 fz0to3un2pr 12441 fzo01 12550 bcp1nk 13104 arisum2 14593 ege2le3 14820 ef4p 14843 efgt1p2 14844 efgt1p 14845 bitsmod 15158 prmdiv 15490 prmdiveq 15491 prmdivdiv 15492 prmreclem2 15621 vdwap1 15681 11prm 15822 631prm 15834 mulgnn0p1 17552 gsummptfzsplitl 18333 iblcnlem1 23554 itgcnlem 23556 dveflem 23742 ply1rem 23923 vieta1lem2 24066 vieta1 24067 pserdvlem2 24182 pserdv2 24184 abelthlem6 24190 abelthlem9 24194 cosne0 24276 logf1o2 24396 logtayl 24406 ang180lem3 24541 birthdaylem2 24679 wilthlem1 24794 ftalem5 24803 ppi2 24896 ppiublem2 24928 ppiub 24929 bclbnd 25005 bposlem2 25010 lgsdir2lem3 25052 lgseisenlem1 25100 axlowdimlem13 25834 spthispth 26622 uhgrwkspthlem2 26650 wwlksnextproplem1 26804 upgr3v3e3cycl 27040 upgr4cycl4dv4e 27045 ballotlemii 30565 ballotlem1c 30569 subfacval2 31169 cvmliftlem5 31271 halffl 39510 fz1ssfz0 39524 sinaover2ne0 40079 stoweidlem11 40228 stoweidlem13 40230 stoweidlem26 40243 stirlinglem7 40297 fourierdlem48 40371 fourierdlem49 40372 fourierdlem69 40392 fourierdlem79 40402 fourierdlem93 40416 etransclem7 40458 etransclem25 40476 etransclem26 40477 etransclem37 40488 iccpartlt 41360 pfx1 41411 31prm 41512 1odd 41811 |
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