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| Mirrors > Home > MPE Home > Th. List > 1e0p1 | Structured version Visualization version GIF version | ||
| Description: The successor of zero. (Contributed by Mario Carneiro, 18-Feb-2014.) |
| Ref | Expression |
|---|---|
| 1e0p1 | ⊢ 1 = (0 + 1) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 0p1e1 12388 | . 2 ⊢ (0 + 1) = 1 | |
| 2 | 1 | eqcomi 2746 | 1 ⊢ 1 = (0 + 1) |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 (class class class)co 7431 0cc0 11155 1c1 11156 + caddc 11158 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-10 2141 ax-11 2157 ax-12 2177 ax-ext 2708 ax-sep 5296 ax-nul 5306 ax-pow 5365 ax-pr 5432 ax-un 7755 ax-resscn 11212 ax-1cn 11213 ax-icn 11214 ax-addcl 11215 ax-addrcl 11216 ax-mulcl 11217 ax-mulrcl 11218 ax-mulcom 11219 ax-addass 11220 ax-mulass 11221 ax-distr 11222 ax-i2m1 11223 ax-1ne0 11224 ax-1rid 11225 ax-rnegex 11226 ax-rrecex 11227 ax-cnre 11228 ax-pre-lttri 11229 ax-pre-lttrn 11230 ax-pre-ltadd 11231 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3or 1088 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-nf 1784 df-sb 2065 df-mo 2540 df-eu 2569 df-clab 2715 df-cleq 2729 df-clel 2816 df-nfc 2892 df-ne 2941 df-nel 3047 df-ral 3062 df-rex 3071 df-rab 3437 df-v 3482 df-sbc 3789 df-csb 3900 df-dif 3954 df-un 3956 df-in 3958 df-ss 3968 df-nul 4334 df-if 4526 df-pw 4602 df-sn 4627 df-pr 4629 df-op 4633 df-uni 4908 df-br 5144 df-opab 5206 df-mpt 5226 df-id 5578 df-po 5592 df-so 5593 df-xp 5691 df-rel 5692 df-cnv 5693 df-co 5694 df-dm 5695 df-rn 5696 df-res 5697 df-ima 5698 df-iota 6514 df-fun 6563 df-fn 6564 df-f 6565 df-f1 6566 df-fo 6567 df-f1o 6568 df-fv 6569 df-ov 7434 df-er 8745 df-en 8986 df-dom 8987 df-sdom 8988 df-pnf 11297 df-mnf 11298 df-ltxr 11300 |
| This theorem is referenced by: 6p5e11 12806 7p4e11 12809 8p3e11 12814 9p2e11 12820 fz1ssfz0 13663 fz0to3un2pr 13669 fzo01 13786 fz01pr 13790 bcp1nk 14356 pfx1 14741 arisum2 15897 ege2le3 16126 ef4p 16149 efgt1p2 16150 efgt1p 16151 bitsmod 16473 prmdiv 16822 prmreclem2 16955 vdwap1 17015 11prm 17152 631prm 17164 mulgnn0p1 19103 gsummptfzsplitl 19951 itgcnlem 25825 dveflem 26017 ply1rem 26205 vieta1lem2 26353 vieta1 26354 pserdvlem2 26472 pserdv2 26474 abelthlem6 26480 abelthlem9 26484 cosne0 26571 logf1o2 26692 logtayl 26702 ang180lem3 26854 birthdaylem2 26995 ftalem5 27120 ppi2 27213 ppiublem2 27247 ppiub 27248 bclbnd 27324 bposlem2 27329 lgsdir2lem3 27371 lgseisenlem1 27419 axlowdimlem13 28969 spthispth 29744 uhgrwkspthlem2 29774 cyclnumvtx 29820 upgr3v3e3cycl 30199 upgr4cycl4dv4e 30204 ballotlemii 34506 ballotlem1c 34510 subfacval2 35192 cvmliftlem5 35294 aks6d1c5lem1 42137 sticksstones11 42157 sticksstones12 42159 metakunt24 42229 3cubeslem1 42695 halffl 45308 sinaover2ne0 45883 stoweidlem11 46026 stoweidlem13 46028 stirlinglem7 46095 fourierdlem48 46169 fourierdlem49 46170 fourierdlem69 46190 fourierdlem79 46200 fourierdlem93 46214 etransclem7 46256 etransclem25 46274 etransclem26 46275 etransclem37 46286 tworepnotupword 46901 iccpartlt 47411 31prm 47584 1odd 48087 itcoval1 48584 ackval1 48602 ackval41a 48615 |
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