Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ wa 395
∨ wo 844 = wceq 1533
∈ wcel 2098 ≠
wne 2932 ∀wral 3053
⊆ wss 3941
Cℋ cch 30676 0ℋc0h 30682 HAtomscat 30712 |
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 2163 ax-ext 2695 ax-rep 5276 ax-sep 5290 ax-nul 5297 ax-pow 5354 ax-pr 5418 ax-un 7719 ax-cnex 11163 ax-resscn 11164 ax-1cn 11165 ax-icn 11166 ax-addcl 11167 ax-addrcl 11168 ax-mulcl 11169 ax-mulrcl 11170 ax-mulcom 11171 ax-addass 11172 ax-mulass 11173 ax-distr 11174 ax-i2m1 11175 ax-1ne0 11176 ax-1rid 11177 ax-rnegex 11178 ax-rrecex 11179 ax-cnre 11180 ax-pre-lttri 11181 ax-pre-lttrn 11182 ax-pre-ltadd 11183 ax-pre-mulgt0 11184 ax-pre-sup 11185 ax-addf 11186 ax-mulf 11187 ax-hilex 30746 ax-hfvadd 30747 ax-hvcom 30748 ax-hvass 30749 ax-hv0cl 30750 ax-hvaddid 30751 ax-hfvmul 30752 ax-hvmulid 30753 ax-hvmulass 30754 ax-hvdistr1 30755 ax-hvdistr2 30756 ax-hvmul0 30757 ax-hfi 30826 ax-his1 30829 ax-his2 30830 ax-his3 30831 ax-his4 30832 |
This theorem depends on definitions:
df-bi 206 df-an 396
df-or 845 df-3or 1085 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2526 df-eu 2555 df-clab 2702 df-cleq 2716 df-clel 2802 df-nfc 2877 df-ne 2933 df-nel 3039 df-ral 3054 df-rex 3063 df-rmo 3368 df-reu 3369 df-rab 3425 df-v 3468 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 4522 df-pw 4597 df-sn 4622 df-pr 4624 df-op 4628 df-uni 4901 df-iun 4990 df-br 5140 df-opab 5202 df-mpt 5223 df-tr 5257 df-id 5565 df-eprel 5571 df-po 5579 df-so 5580 df-fr 5622 df-we 5624 df-xp 5673 df-rel 5674 df-cnv 5675 df-co 5676 df-dm 5677 df-rn 5678 df-res 5679 df-ima 5680 df-pred 6291 df-ord 6358 df-on 6359 df-lim 6360 df-suc 6361 df-iota 6486 df-fun 6536 df-fn 6537 df-f 6538 df-f1 6539 df-fo 6540 df-f1o 6541 df-fv 6542 df-riota 7358 df-ov 7405 df-oprab 7406 df-mpo 7407 df-om 7850 df-1st 7969 df-2nd 7970 df-frecs 8262 df-wrecs 8293 df-recs 8367 df-rdg 8406 df-er 8700 df-map 8819 df-pm 8820 df-en 8937 df-dom 8938 df-sdom 8939 df-sup 9434 df-inf 9435 df-pnf 11249 df-mnf 11250 df-xr 11251 df-ltxr 11252 df-le 11253 df-sub 11445 df-neg 11446 df-div 11871 df-nn 12212 df-2 12274
df-3 12275 df-4 12276
df-n0 12472 df-z 12558
df-uz 12822 df-q 12932
df-rp 12976 df-xneg 13093 df-xadd 13094 df-xmul 13095 df-icc 13332 df-seq 13968 df-exp 14029 df-cj 15048 df-re 15049 df-im 15050 df-sqrt 15184 df-abs 15185 df-topgen 17394 df-psmet 21226 df-xmet 21227 df-met 21228 df-bl 21229 df-mopn 21230 df-top 22740 df-topon 22757 df-bases 22793 df-lm 23077 df-haus 23163 df-grpo 30240 df-gid 30241 df-ginv 30242 df-gdiv 30243 df-ablo 30292 df-vc 30306 df-nv 30339 df-va 30342 df-ba 30343 df-sm 30344 df-0v 30345 df-vs 30346 df-nmcv 30347 df-ims 30348 df-hnorm 30715 df-hvsub 30718 df-hlim 30719 df-sh 30954 df-ch 30968 df-ch0 31000 df-cv 32026 df-at 32085 |
This theorem is referenced by: atsseq
32094 hatomistici
32109 atssma
32125 chirredlem1
32137 chirredi
32141 |