Colors of
variables: wff
setvar class |
Syntax hints:
β wi 4 β§ wa 394
β wcel 2098 β
wss 3939 {csn 4624
βcfv 6543
βchba 30773 spancspn 30786 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905
ax-6 1963 ax-7 2003 ax-8 2100
ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2166 ax-ext 2696 ax-rep 5280 ax-sep 5294 ax-nul 5301 ax-pow 5359 ax-pr 5423 ax-un 7738 ax-cnex 11194 ax-resscn 11195 ax-1cn 11196 ax-icn 11197 ax-addcl 11198 ax-addrcl 11199 ax-mulcl 11200 ax-mulrcl 11201 ax-mulcom 11202 ax-addass 11203 ax-mulass 11204 ax-distr 11205 ax-i2m1 11206 ax-1ne0 11207 ax-1rid 11208 ax-rnegex 11209 ax-rrecex 11210 ax-cnre 11211 ax-pre-lttri 11212 ax-pre-lttrn 11213 ax-pre-ltadd 11214 ax-pre-mulgt0 11215 ax-pre-sup 11216 ax-addf 11217 ax-mulf 11218 ax-hilex 30853 ax-hfvadd 30854 ax-hvcom 30855 ax-hvass 30856 ax-hv0cl 30857 ax-hvaddid 30858 ax-hfvmul 30859 ax-hvmulid 30860 ax-hvmulass 30861 ax-hvdistr1 30862 ax-hvdistr2 30863 ax-hvmul0 30864 ax-hfi 30933 ax-his1 30936 ax-his2 30937 ax-his3 30938 ax-his4 30939 |
This theorem depends on definitions:
df-bi 206 df-an 395
df-or 846 df-3or 1085 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2528 df-eu 2557 df-clab 2703 df-cleq 2717 df-clel 2802 df-nfc 2877 df-ne 2931 df-nel 3037 df-ral 3052 df-rex 3061 df-rmo 3364 df-reu 3365 df-rab 3420 df-v 3465 df-sbc 3769 df-csb 3885 df-dif 3942 df-un 3944 df-in 3946 df-ss 3956 df-pss 3959 df-nul 4319 df-if 4525 df-pw 4600 df-sn 4625 df-pr 4627 df-op 4631 df-uni 4904 df-int 4945 df-iun 4993 df-br 5144 df-opab 5206 df-mpt 5227 df-tr 5261 df-id 5570 df-eprel 5576 df-po 5584 df-so 5585 df-fr 5627 df-we 5629 df-xp 5678 df-rel 5679 df-cnv 5680 df-co 5681 df-dm 5682 df-rn 5683 df-res 5684 df-ima 5685 df-pred 6300 df-ord 6367 df-on 6368 df-lim 6369 df-suc 6370 df-iota 6495 df-fun 6545 df-fn 6546 df-f 6547 df-f1 6548 df-fo 6549 df-f1o 6550 df-fv 6551 df-riota 7372 df-ov 7419 df-oprab 7420 df-mpo 7421 df-om 7869 df-1st 7991 df-2nd 7992 df-frecs 8285 df-wrecs 8316 df-recs 8390 df-rdg 8429 df-er 8723 df-map 8845 df-pm 8846 df-en 8963 df-dom 8964 df-sdom 8965 df-sup 9465 df-inf 9466 df-pnf 11280 df-mnf 11281 df-xr 11282 df-ltxr 11283 df-le 11284 df-sub 11476 df-neg 11477 df-div 11902 df-nn 12243 df-2 12305
df-3 12306 df-4 12307
df-n0 12503 df-z 12589
df-uz 12853 df-q 12963
df-rp 13007 df-xneg 13124 df-xadd 13125 df-xmul 13126 df-icc 13363 df-seq 13999 df-exp 14059 df-cj 15078 df-re 15079 df-im 15080 df-sqrt 15214 df-abs 15215 df-topgen 17424 df-psmet 21275 df-xmet 21276 df-met 21277 df-bl 21278 df-mopn 21279 df-top 22814 df-topon 22831 df-bases 22867 df-lm 23151 df-haus 23237 df-grpo 30347 df-gid 30348 df-ginv 30349 df-gdiv 30350 df-ablo 30399 df-vc 30413 df-nv 30446 df-va 30449 df-ba 30450 df-sm 30451 df-0v 30452 df-vs 30453 df-nmcv 30454 df-ims 30455 df-hnorm 30822 df-hvsub 30825 df-hlim 30826 df-sh 31061 df-ch 31075 df-ch0 31107 df-span 31163 |
This theorem is referenced by: sumdmdlem
32272 |