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Mirrors > Home > MPE Home > Th. List > tdrgunit | Structured version Visualization version Unicode version |
Description: The unit group of a topological division ring is a topological group. (Contributed by Mario Carneiro, 5-Oct-2015.) |
Ref | Expression |
---|---|
istrg.1 | mulGrp |
istdrg.1 | Unit |
Ref | Expression |
---|---|
tdrgunit | TopDRing ↾s |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | istrg.1 | . . 3 mulGrp | |
2 | istdrg.1 | . . 3 Unit | |
3 | 1, 2 | istdrg 21969 | . 2 TopDRing ↾s |
4 | 3 | simp3bi 1078 | 1 TopDRing ↾s |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 cfv 5888 (class class class)co 6650 ↾s cress 15858 mulGrpcmgp 18489 Unitcui 18639 cdr 18747 ctgp 21875 ctrg 21959 TopDRingctdrg 21960 |
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-ov 6653 df-tdrg 21964 |
This theorem is referenced by: invrcn2 21983 |
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