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Mirrors > Home > HSE Home > Th. List > chjcl | Structured version Visualization version Unicode version |
Description: Closure of join in ![]() |
Ref | Expression |
---|---|
chjcl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | chsh 26877 |
. 2
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2 | chsh 26877 |
. 2
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3 | shjcl 27009 |
. 2
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4 | 1, 2, 3 | syl2an 480 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-8 1889 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-rep 4515 ax-sep 4525 ax-nul 4534 ax-pow 4581 ax-pr 4639 ax-un 6583 ax-inf2 8146 ax-cnex 9595 ax-resscn 9596 ax-1cn 9597 ax-icn 9598 ax-addcl 9599 ax-addrcl 9600 ax-mulcl 9601 ax-mulrcl 9602 ax-mulcom 9603 ax-addass 9604 ax-mulass 9605 ax-distr 9606 ax-i2m1 9607 ax-1ne0 9608 ax-1rid 9609 ax-rnegex 9610 ax-rrecex 9611 ax-cnre 9612 ax-pre-lttri 9613 ax-pre-lttrn 9614 ax-pre-ltadd 9615 ax-pre-mulgt0 9616 ax-pre-sup 9617 ax-addf 9618 ax-mulf 9619 ax-hilex 26652 ax-hfvadd 26653 ax-hvcom 26654 ax-hvass 26655 ax-hv0cl 26656 ax-hvaddid 26657 ax-hfvmul 26658 ax-hvmulid 26659 ax-hvmulass 26660 ax-hvdistr1 26661 ax-hvdistr2 26662 ax-hvmul0 26663 ax-hfi 26732 ax-his1 26735 ax-his2 26736 ax-his3 26737 ax-his4 26738 ax-hcompl 26855 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 986 df-3an 987 df-tru 1447 df-fal 1450 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-nel 2625 df-ral 2742 df-rex 2743 df-reu 2744 df-rmo 2745 df-rab 2746 df-v 3047 df-sbc 3268 df-csb 3364 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-pss 3420 df-nul 3732 df-if 3882 df-pw 3953 df-sn 3969 df-pr 3971 df-tp 3973 df-op 3975 df-uni 4199 df-int 4235 df-iun 4280 df-iin 4281 df-br 4403 df-opab 4462 df-mpt 4463 df-tr 4498 df-eprel 4745 df-id 4749 df-po 4755 df-so 4756 df-fr 4793 df-se 4794 df-we 4795 df-xp 4840 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-rn 4845 df-res 4846 df-ima 4847 df-pred 5380 df-ord 5426 df-on 5427 df-lim 5428 df-suc 5429 df-iota 5546 df-fun 5584 df-fn 5585 df-f 5586 df-f1 5587 df-fo 5588 df-f1o 5589 df-fv 5590 df-isom 5591 df-riota 6252 df-ov 6293 df-oprab 6294 df-mpt2 6295 df-of 6531 df-om 6693 df-1st 6793 df-2nd 6794 df-supp 6915 df-wrecs 7028 df-recs 7090 df-rdg 7128 df-1o 7182 df-2o 7183 df-oadd 7186 df-er 7363 df-map 7474 df-pm 7475 df-ixp 7523 df-en 7570 df-dom 7571 df-sdom 7572 df-fin 7573 df-fsupp 7884 df-fi 7925 df-sup 7956 df-inf 7957 df-oi 8025 df-card 8373 df-cda 8598 df-pnf 9677 df-mnf 9678 df-xr 9679 df-ltxr 9680 df-le 9681 df-sub 9862 df-neg 9863 df-div 10270 df-nn 10610 df-2 10668 df-3 10669 df-4 10670 df-5 10671 df-6 10672 df-7 10673 df-8 10674 df-9 10675 df-10 10676 df-n0 10870 df-z 10938 df-dec 11052 df-uz 11160 df-q 11265 df-rp 11303 df-xneg 11409 df-xadd 11410 df-xmul 11411 df-ioo 11639 df-icc 11642 df-fz 11785 df-fzo 11916 df-seq 12214 df-exp 12273 df-hash 12516 df-cj 13162 df-re 13163 df-im 13164 df-sqrt 13298 df-abs 13299 df-clim 13552 df-sum 13753 df-struct 15123 df-ndx 15124 df-slot 15125 df-base 15126 df-sets 15127 df-ress 15128 df-plusg 15203 df-mulr 15204 df-starv 15205 df-sca 15206 df-vsca 15207 df-ip 15208 df-tset 15209 df-ple 15210 df-ds 15212 df-unif 15213 df-hom 15214 df-cco 15215 df-rest 15321 df-topn 15322 df-0g 15340 df-gsum 15341 df-topgen 15342 df-pt 15343 df-prds 15346 df-xrs 15400 df-qtop 15406 df-imas 15407 df-xps 15410 df-mre 15492 df-mrc 15493 df-acs 15495 df-mgm 16488 df-sgrp 16527 df-mnd 16537 df-submnd 16583 df-mulg 16676 df-cntz 16971 df-cmn 17432 df-psmet 18962 df-xmet 18963 df-met 18964 df-bl 18965 df-mopn 18966 df-cnfld 18971 df-top 19921 df-bases 19922 df-topon 19923 df-topsp 19924 df-cn 20243 df-cnp 20244 df-lm 20245 df-haus 20331 df-tx 20577 df-hmeo 20770 df-xms 21335 df-ms 21336 df-tms 21337 df-cau 22226 df-grpo 25919 df-gid 25920 df-ginv 25921 df-gdiv 25922 df-ablo 26010 df-vc 26165 df-nv 26211 df-va 26214 df-ba 26215 df-sm 26216 df-0v 26217 df-vs 26218 df-nmcv 26219 df-ims 26220 df-dip 26337 df-hnorm 26621 df-hvsub 26624 df-hlim 26625 df-hcau 26626 df-sh 26860 df-ch 26874 df-oc 26905 df-chj 26963 |
This theorem is referenced by: chj4 27188 cm0 27262 pjoml5 27266 fh1 27271 fh2 27272 cm2j 27273 spansnscl 27301 hstle 27883 strlem3a 27905 hstrlem3a 27913 spansncv2 27946 mdbr2 27949 dmdmd 27953 dmdbr3 27958 dmdbr4 27959 dmdbr5 27961 mdsl1i 27974 mdsl2i 27975 mdslmd1i 27982 mdexchi 27988 cvdmd 27990 chcv1 28008 cvati 28019 cvexchlem 28021 atcv0eq 28032 atexch 28034 atomli 28035 atcvatlem 28038 atcvat2i 28040 chirredlem3 28045 atcvat3i 28049 atcvat4i 28050 mdsymlem1 28056 mdsymlem3 28058 mdsymlem5 28060 mdsymlem6 28061 dmdbr5ati 28075 |
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