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Mirrors > Home > MPE Home > Th. List > tgpinv | Structured version Visualization version Unicode version |
Description: In a topological group, the inverse function is continuous. (Contributed by FL, 21-Jun-2010.) (Revised by FL, 27-Jun-2014.) |
Ref | Expression |
---|---|
tgpcn.j | |
tgpinv.5 |
Ref | Expression |
---|---|
tgpinv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tgpcn.j | . . 3 | |
2 | tgpinv.5 | . . 3 | |
3 | 1, 2 | istgp 21881 | . 2 TopMnd |
4 | 3 | simp3bi 1078 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 cfv 5888 (class class class)co 6650 ctopn 16082 cgrp 17422 cminusg 17423 ccn 21028 TopMndctmd 21874 ctgp 21875 |
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 ax-nul 4789 |
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-eu 2474 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 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-tgp 21877 |
This theorem is referenced by: grpinvhmeo 21890 tgpsubcn 21894 tgpmulg 21897 oppgtgp 21902 subgtgp 21909 prdstgpd 21928 tsmsinv 21951 invrcn2 21983 |
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