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Mirrors > Home > MPE Home > Th. List > Mathboxes > isdmn2 | Structured version Visualization version Unicode version |
Description: The predicate "is a domain". (Contributed by Jeff Madsen, 10-Jun-2010.) |
Ref | Expression |
---|---|
isdmn2 | CRingOps |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isdmn 33853 | . 2 | |
2 | prrngorngo 33850 | . . . 4 | |
3 | iscrngo 33795 | . . . . 5 CRingOps | |
4 | 3 | baibr 945 | . . . 4 CRingOps |
5 | 2, 4 | syl 17 | . . 3 CRingOps |
6 | 5 | pm5.32i 669 | . 2 CRingOps |
7 | 1, 6 | bitri 264 | 1 CRingOps |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wcel 1990 crngo 33693 ccm2 33788 CRingOpsccring 33792 cprrng 33845 cdmn 33846 |
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-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-crngo 33793 df-prrngo 33847 df-dmn 33848 |
This theorem is referenced by: dmncrng 33855 flddmn 33857 isdmn3 33873 |
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