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Mirrors > Home > MPE Home > Th. List > negneg1e1 | Structured version Visualization version GIF version |
Description: --1 is 1. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
negneg1e1 | ⊢ --1 = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1cn 10686 | . 2 ⊢ 1 ∈ ℂ | |
2 | 1 | negnegi 11047 | 1 ⊢ --1 = 1 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 1c1 10629 -cneg 10962 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2162 ax-12 2179 ax-ext 2711 ax-sep 5177 ax-nul 5184 ax-pow 5242 ax-pr 5306 ax-un 7492 ax-resscn 10685 ax-1cn 10686 ax-icn 10687 ax-addcl 10688 ax-addrcl 10689 ax-mulcl 10690 ax-mulrcl 10691 ax-mulcom 10692 ax-addass 10693 ax-mulass 10694 ax-distr 10695 ax-i2m1 10696 ax-1ne0 10697 ax-1rid 10698 ax-rnegex 10699 ax-rrecex 10700 ax-cnre 10701 ax-pre-lttri 10702 ax-pre-lttrn 10703 ax-pre-ltadd 10704 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 847 df-3or 1089 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1787 df-nf 1791 df-sb 2075 df-mo 2541 df-eu 2571 df-clab 2718 df-cleq 2731 df-clel 2812 df-nfc 2882 df-ne 2936 df-nel 3040 df-ral 3059 df-rex 3060 df-reu 3061 df-rab 3063 df-v 3402 df-sbc 3686 df-csb 3801 df-dif 3856 df-un 3858 df-in 3860 df-ss 3870 df-nul 4222 df-if 4425 df-pw 4500 df-sn 4527 df-pr 4529 df-op 4533 df-uni 4807 df-br 5041 df-opab 5103 df-mpt 5121 df-id 5439 df-po 5452 df-so 5453 df-xp 5541 df-rel 5542 df-cnv 5543 df-co 5544 df-dm 5545 df-rn 5546 df-res 5547 df-ima 5548 df-iota 6308 df-fun 6352 df-fn 6353 df-f 6354 df-f1 6355 df-fo 6356 df-f1o 6357 df-fv 6358 df-riota 7140 df-ov 7186 df-oprab 7187 df-mpo 7188 df-er 8333 df-en 8569 df-dom 8570 df-sdom 8571 df-pnf 10768 df-mnf 10769 df-ltxr 10771 df-sub 10963 df-neg 10964 |
This theorem is referenced by: m1expcl2 13556 absi 14749 sinhval 15612 coshval 15613 xrhmeo 23711 ncvspi 23921 cphipval2 24006 atandm2 25628 efiasin 25639 asinsinlem 25642 asin1 25645 nvpi 28615 ipasslem10 28787 hvaddsubval 28981 polid2i 29105 lnophmlem2 29965 dvasin 35517 |
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