Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > 1p0e1 | Structured version Visualization version GIF version |
Description: 1 + 0 = 1. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
1p0e1 | ⊢ (1 + 0) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1cn 10784 | . 2 ⊢ 1 ∈ ℂ | |
2 | 1 | addid1i 11016 | 1 ⊢ (1 + 0) = 1 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1543 (class class class)co 7210 0cc0 10726 1c1 10727 + caddc 10729 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2158 ax-12 2175 ax-ext 2708 ax-sep 5189 ax-nul 5196 ax-pow 5255 ax-pr 5319 ax-un 7520 ax-resscn 10783 ax-1cn 10784 ax-icn 10785 ax-addcl 10786 ax-addrcl 10787 ax-mulcl 10788 ax-mulrcl 10789 ax-mulcom 10790 ax-addass 10791 ax-mulass 10792 ax-distr 10793 ax-i2m1 10794 ax-1ne0 10795 ax-1rid 10796 ax-rnegex 10797 ax-rrecex 10798 ax-cnre 10799 ax-pre-lttri 10800 ax-pre-lttrn 10801 ax-pre-ltadd 10802 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-3or 1090 df-3an 1091 df-tru 1546 df-fal 1556 df-ex 1788 df-nf 1792 df-sb 2071 df-mo 2539 df-eu 2568 df-clab 2715 df-cleq 2729 df-clel 2816 df-nfc 2886 df-ne 2940 df-nel 3044 df-ral 3063 df-rex 3064 df-rab 3067 df-v 3407 df-sbc 3692 df-csb 3809 df-dif 3866 df-un 3868 df-in 3870 df-ss 3880 df-nul 4235 df-if 4437 df-pw 4512 df-sn 4539 df-pr 4541 df-op 4545 df-uni 4817 df-br 5051 df-opab 5113 df-mpt 5133 df-id 5452 df-po 5465 df-so 5466 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 6335 df-fun 6379 df-fn 6380 df-f 6381 df-f1 6382 df-fo 6383 df-f1o 6384 df-fv 6385 df-ov 7213 df-er 8388 df-en 8624 df-dom 8625 df-sdom 8626 df-pnf 10866 df-mnf 10867 df-ltxr 10869 |
This theorem is referenced by: xov1plusxeqvd 13083 bernneq 13793 bcpasc 13884 relexpaddg 14613 4sqlem19 16513 1259lem1 16681 2503lem2 16688 ef2pi 25364 dvsqrt 25625 dvcnsqrt 25627 loglesqrt 25641 efrlim 25849 basellem7 25966 1sgm2ppw 26078 addsqnreup 26321 chpchtlim 26357 axlowdimlem16 27045 vc0 28652 ballotlemic 32182 hgt750lemd 32337 divcnvlin 33413 faclim 33427 poimirlem16 35528 poimirlem31 35543 12gcd5e1 39743 3exp7 39793 sticksstones7 39828 sticksstones12a 39833 sticksstones12 39834 metakunt29 39873 3cubeslem1 40207 pell1qr1 40394 pell1qrgaplem 40396 rmxy0 40446 binomcxplemnotnn0 41645 clim1fr1 42815 dvxpaek 43154 itgiccshift 43194 itgperiod 43195 wallispi2lem2 43286 |
Copyright terms: Public domain | W3C validator |