Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > rrexttps | Structured version Visualization version Unicode version |
Description: An extension of is a topological space. (Contributed by Thierry Arnoux, 7-Sep-2018.) |
Ref | Expression |
---|---|
rrexttps | ℝExt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rrextnrg 30045 | . . 3 ℝExt NrmRing | |
2 | nrgngp 22466 | . . 3 NrmRing NrmGrp | |
3 | ngpxms 22405 | . . 3 NrmGrp | |
4 | 1, 2, 3 | 3syl 18 | . 2 ℝExt |
5 | xmstps 22258 | . 2 | |
6 | 4, 5 | syl 17 | 1 ℝExt |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 ctps 20736 cxme 22122 NrmGrpcngp 22382 NrmRingcnrg 22384 ℝExt crrext 30038 |
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-opab 4713 df-xp 5120 df-co 5123 df-res 5126 df-iota 5851 df-fv 5896 df-xms 22125 df-ms 22126 df-ngp 22388 df-nrg 22390 df-rrext 30043 |
This theorem is referenced by: (None) |
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