| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 ↔ wb 205
∧ wa 395 ∈
wcel 2105 ≠ wne 2939
∅c0 4322 ‘cfv 6543 Fincfn 8942
ℕcn 12217 ♯chash 14295 Word cword 14469 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912
ax-6 1970 ax-7 2010 ax-8 2107
ax-9 2115 ax-10 2136 ax-11 2153 ax-12 2170 ax-ext 2702 ax-rep 5285 ax-sep 5299 ax-nul 5306 ax-pow 5363 ax-pr 5427 ax-un 7728 ax-cnex 11169 ax-resscn 11170 ax-1cn 11171 ax-icn 11172 ax-addcl 11173 ax-addrcl 11174 ax-mulcl 11175 ax-mulrcl 11176 ax-mulcom 11177 ax-addass 11178 ax-mulass 11179 ax-distr 11180 ax-i2m1 11181 ax-1ne0 11182 ax-1rid 11183 ax-rnegex 11184 ax-rrecex 11185 ax-cnre 11186 ax-pre-lttri 11187 ax-pre-lttrn 11188 ax-pre-ltadd 11189 ax-pre-mulgt0 11190 |
| This theorem depends on definitions:
df-bi 206 df-an 396
df-or 845 df-3or 1087 df-3an 1088 df-tru 1543 df-fal 1553 df-ex 1781 df-nf 1785 df-sb 2067 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-reu 3376 df-rab 3432 df-v 3475 df-sbc 3778 df-csb 3894 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-pss 3967 df-nul 4323 df-if 4529 df-pw 4604 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-int 4951 df-iun 4999 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5574 df-eprel 5580 df-po 5588 df-so 5589 df-fr 5631 df-we 5633 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-rn 5687 df-res 5688 df-ima 5689 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 7368 df-ov 7415 df-oprab 7416 df-mpo 7417 df-om 7859 df-1st 7978 df-2nd 7979 df-frecs 8269 df-wrecs 8300 df-recs 8374 df-rdg 8413 df-1o 8469 df-er 8706 df-en 8943 df-dom 8944 df-sdom 8945 df-fin 8946 df-card 9937 df-pnf 11255 df-mnf 11256 df-xr 11257 df-ltxr 11258 df-le 11259 df-sub 11451 df-neg 11452 df-nn 12218 df-n0 12478 df-z 12564
df-uz 12828 df-fz 13490 df-fzo 13633 df-hash 14296 df-word 14470 |
| This theorem is referenced by: len0nnbi
14506 lswcl
14523 ccatval1lsw
14539 ccatval21sw
14540 lswccatn0lsw
14546 ccat1st1st
14583 pfxtrcfv
14648 pfxsuff1eqwrdeq
14654 pfx1
14658 wrdeqs1cat
14675 cshw0
14749 cshwmodn
14750 cshwn
14752 cshwlen
14754 cshwidx0mod
14760 scshwfzeqfzo
14782 lswco
14795 gsumwsubmcl
18755 gsumsgrpccat
18758 efgsf
19639 efgsrel
19644 efgs1b
19646 efgredlema
19650 efgredlemd
19654 efgrelexlemb
19660 clwwlkccatlem
29510 clwwlkwwlksb
29575 cycpmrn
32573 signsvtn0
33880 signstfvneq0
33882 signsvfn
33892 signsvtp
33893 signsvtn
33894 signsvfpn
33895 signsvfnn
33896 signlem0
33897 |
