Colors of
variables: wff
setvar class |
Syntax hints:
β§ w3a 1086 = wceq 1540
Vcvv 3473 β© cin 3947
β
c0 4322 {cpr 4630
class class class wbr 5148 β‘ccnv 5675
βΎ cres 5678 β
cima 5679 Rel wrel 5681
Fun wfun 6537 βcfv 6543 (class class class)co 7412
0cc0 11116 1c1 11117
..^cfzo 13634 β―chash 14297 Trailsctrls 29381 Pathscpths 29403 |
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-sep 5299 ax-nul 5306 ax-pr 5427 |
This theorem depends on definitions:
df-bi 206 df-an 396
df-or 845 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-ral 3061 df-rex 3070 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-nul 4323 df-if 4529 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-br 5149 df-opab 5211 df-mpt 5232 df-id 5574 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-iota 6495 df-fun 6545 df-fv 6551 df-pths 29407 |
This theorem is referenced by: iscycl
29482 cyclnspth
29491 |