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Mirrors > Home > MPE Home > Th. List > nzrring | Structured version Visualization version Unicode version |
Description: A nonzero ring is a ring. (Contributed by Stefan O'Rear, 24-Feb-2015.) |
Ref | Expression |
---|---|
nzrring | NzRing |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2622 | . . 3 | |
2 | eqid 2622 | . . 3 | |
3 | 1, 2 | isnzr 19259 | . 2 NzRing |
4 | 3 | simplbi 476 | 1 NzRing |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 wne 2794 cfv 5888 c0g 16100 cur 18501 crg 18547 NzRingcnzr 19257 |
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-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-nzr 19258 |
This theorem is referenced by: opprnzr 19265 nzrunit 19267 domnring 19296 domnchr 19880 uvcf1 20131 lindfind2 20157 frlmisfrlm 20187 nminvr 22473 deg1pw 23880 ply1nz 23881 ply1remlem 23922 ply1rem 23923 facth1 23924 fta1glem1 23925 fta1glem2 23926 zrhnm 30013 mon1pid 37783 mon1psubm 37784 nzrneg1ne0 41869 islindeps2 42272 |
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