Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
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 11747 | . 2 ⊢ (0 + 1) = 1 | |
2 | 1 | eqcomi 2827 | 1 ⊢ 1 = (0 + 1) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 (class class class)co 7145 0cc0 10525 1c1 10526 + caddc 10528 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-sep 5194 ax-nul 5201 ax-pow 5257 ax-pr 5320 ax-un 7450 ax-resscn 10582 ax-1cn 10583 ax-icn 10584 ax-addcl 10585 ax-addrcl 10586 ax-mulcl 10587 ax-mulrcl 10588 ax-mulcom 10589 ax-addass 10590 ax-mulass 10591 ax-distr 10592 ax-i2m1 10593 ax-1ne0 10594 ax-1rid 10595 ax-rnegex 10596 ax-rrecex 10597 ax-cnre 10598 ax-pre-lttri 10599 ax-pre-lttrn 10600 ax-pre-ltadd 10601 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-3or 1080 df-3an 1081 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-mo 2615 df-eu 2647 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-ne 3014 df-nel 3121 df-ral 3140 df-rex 3141 df-rab 3144 df-v 3494 df-sbc 3770 df-csb 3881 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-nul 4289 df-if 4464 df-pw 4537 df-sn 4558 df-pr 4560 df-op 4564 df-uni 4831 df-br 5058 df-opab 5120 df-mpt 5138 df-id 5453 df-po 5467 df-so 5468 df-xp 5554 df-rel 5555 df-cnv 5556 df-co 5557 df-dm 5558 df-rn 5559 df-res 5560 df-ima 5561 df-iota 6307 df-fun 6350 df-fn 6351 df-f 6352 df-f1 6353 df-fo 6354 df-f1o 6355 df-fv 6356 df-ov 7148 df-er 8278 df-en 8498 df-dom 8499 df-sdom 8500 df-pnf 10665 df-mnf 10666 df-ltxr 10668 |
This theorem is referenced by: 6p5e11 12159 7p4e11 12162 8p3e11 12167 9p2e11 12173 fz1ssfz0 12991 fz0to3un2pr 12997 fzo01 13107 bcp1nk 13665 pfx1 14053 arisum2 15204 ege2le3 15431 ef4p 15454 efgt1p2 15455 efgt1p 15456 bitsmod 15773 prmdiv 16110 prmreclem2 16241 vdwap1 16301 11prm 16436 631prm 16448 mulgnn0p1 18177 gsummptfzsplitl 18982 itgcnlem 24317 dveflem 24503 ply1rem 24684 vieta1lem2 24827 vieta1 24828 pserdvlem2 24943 pserdv2 24945 abelthlem6 24951 abelthlem9 24955 cosne0 25041 logf1o2 25160 logtayl 25170 ang180lem3 25316 birthdaylem2 25457 ftalem5 25581 ppi2 25674 ppiublem2 25706 ppiub 25707 bclbnd 25783 bposlem2 25788 lgsdir2lem3 25830 lgseisenlem1 25878 axlowdimlem13 26667 spthispth 27434 uhgrwkspthlem2 27462 upgr3v3e3cycl 27886 upgr4cycl4dv4e 27891 ballotlemii 31660 ballotlem1c 31664 subfacval2 32331 cvmliftlem5 32433 3cubeslem1 39159 halffl 41439 sinaover2ne0 42025 stoweidlem11 42173 stoweidlem13 42175 stirlinglem7 42242 fourierdlem48 42316 fourierdlem49 42317 fourierdlem69 42337 fourierdlem79 42347 fourierdlem93 42361 etransclem7 42403 etransclem25 42421 etransclem26 42422 etransclem37 42433 iccpartlt 43461 31prm 43637 1odd 43955 |
Copyright terms: Public domain | W3C validator |