| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 ∈ wcel 2106
‘cfv 6529 TopSpctps 22358
NrmGrpcngp 24010 ℝ^crrx 24824 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913
ax-6 1971 ax-7 2011 ax-8 2108
ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2702 ax-rep 5275 ax-sep 5289 ax-nul 5296 ax-pow 5353 ax-pr 5417 ax-un 7705 ax-inf2 9615 ax-cnex 11145 ax-resscn 11146 ax-1cn 11147 ax-icn 11148 ax-addcl 11149 ax-addrcl 11150 ax-mulcl 11151 ax-mulrcl 11152 ax-mulcom 11153 ax-addass 11154 ax-mulass 11155 ax-distr 11156 ax-i2m1 11157 ax-1ne0 11158 ax-1rid 11159 ax-rnegex 11160 ax-rrecex 11161 ax-cnre 11162 ax-pre-lttri 11163 ax-pre-lttrn 11164 ax-pre-ltadd 11165 ax-pre-mulgt0 11166 ax-pre-sup 11167 ax-addf 11168 ax-mulf 11169 |
| This theorem depends on definitions:
df-bi 206 df-an 397
df-or 846 df-3or 1088 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2533 df-eu 2562 df-clab 2709 df-cleq 2723 df-clel 2809 df-nfc 2884 df-ne 2940 df-nel 3046 df-ral 3061 df-rex 3070 df-rmo 3375 df-reu 3376 df-rab 3430 df-v 3472 df-sbc 3771 df-csb 3887 df-dif 3944 df-un 3946 df-in 3948 df-ss 3958 df-pss 3960 df-nul 4316 df-if 4520 df-pw 4595 df-sn 4620 df-pr 4622 df-tp 4624 df-op 4626 df-uni 4899 df-int 4941 df-iun 4989 df-br 5139 df-opab 5201 df-mpt 5222 df-tr 5256 df-id 5564 df-eprel 5570 df-po 5578 df-so 5579 df-fr 5621 df-se 5622 df-we 5623 df-xp 5672 df-rel 5673 df-cnv 5674 df-co 5675 df-dm 5676 df-rn 5677 df-res 5678 df-ima 5679 df-pred 6286 df-ord 6353 df-on 6354 df-lim 6355 df-suc 6356 df-iota 6481 df-fun 6531 df-fn 6532 df-f 6533 df-f1 6534 df-fo 6535 df-f1o 6536 df-fv 6537 df-isom 6538 df-riota 7346 df-ov 7393 df-oprab 7394 df-mpo 7395 df-of 7650 df-om 7836 df-1st 7954 df-2nd 7955 df-supp 8126 df-tpos 8190 df-frecs 8245 df-wrecs 8276 df-recs 8350 df-rdg 8389 df-1o 8445 df-er 8683 df-map 8802 df-ixp 8872 df-en 8920 df-dom 8921 df-sdom 8922 df-fin 8923 df-fsupp 9342 df-sup 9416 df-inf 9417 df-oi 9484 df-card 9913 df-pnf 11229 df-mnf 11230 df-xr 11231 df-ltxr 11232 df-le 11233 df-sub 11425 df-neg 11426 df-div 11851 df-nn 12192 df-2 12254
df-3 12255 df-4 12256
df-5 12257 df-6 12258
df-7 12259 df-8 12260
df-9 12261 df-n0 12452 df-z 12538
df-dec 12657 df-uz 12802 df-q 12912
df-rp 12954 df-xneg 13071 df-xadd 13072 df-xmul 13073 df-ico 13309 df-fz 13464 df-fzo 13607 df-seq 13946 df-exp 14007 df-hash 14270 df-cj 15025 df-re 15026 df-im 15027 df-sqrt 15161 df-abs 15162 df-clim 15411 df-sum 15612 df-struct 17059 df-sets 17076 df-slot 17094 df-ndx 17106 df-base 17124 df-ress 17153 df-plusg 17189 df-mulr 17190 df-starv 17191 df-sca 17192 df-vsca 17193 df-ip 17194 df-tset 17195 df-ple 17196 df-ds 17198 df-unif 17199 df-hom 17200 df-cco 17201 df-rest 17347 df-topn 17348 df-0g 17366 df-gsum 17367 df-topgen 17368 df-prds 17372 df-pws 17374 df-mgm 18540 df-sgrp 18589 df-mnd 18600 df-mhm 18644 df-submnd 18645 df-grp 18794 df-minusg 18795 df-sbg 18796 df-subg 18972 df-ghm 19053 df-cntz 19144 df-cmn 19611 df-abl 19612 df-mgp 19944 df-ur 19961 df-ring 20013 df-cring 20014 df-oppr 20099 df-dvdsr 20120 df-unit 20121 df-invr 20151 df-dvr 20162 df-rnghom 20198 df-drng 20264 df-field 20265 df-subrg 20305 df-abv 20369 df-staf 20397 df-srng 20398 df-lmod 20417 df-lss 20487 df-lmhm 20577 df-lvec 20658 df-sra 20729 df-rgmod 20730 df-psmet 20865 df-xmet 20866 df-met 20867 df-bl 20868 df-mopn 20869 df-cnfld 20874 df-refld 21086 df-phl 21107 df-dsmm 21215 df-frlm 21230 df-top 22320 df-topon 22337 df-topsp 22359 df-bases 22373 df-xms 23750 df-ms 23751 df-nm 24015 df-ngp 24016 df-tng 24017 df-nrg 24018 df-nlm 24019 df-clm 24503 df-cph 24609 df-tcph 24610 df-rrx 24826 |
| This theorem is referenced by: rrxtopon
44763 rrxtop
44764 qndenserrnopnlem
44772 qndenserrn
44774 |
