| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 ∈ wcel 2105
UHGraphcuhgr 28584 UPGraphcupgr 28608 UMGraphcumgr 28609 |
| 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-pow 5363 ax-pr 5427 ax-un 7728 ax-resscn 11170 ax-1cn 11171 ax-icn 11172 ax-addcl 11173 ax-addrcl 11174 ax-mulcl 11175 ax-mulrcl 11176 ax-i2m1 11181 ax-1ne0 11182 ax-rrecex 11185 ax-cnre 11186 ax-pre-lttri 11187 |
| 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-ne 2940 df-nel 3046 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-pw 4604 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-fn 6546 df-f 6547 df-f1 6548 df-fo 6549 df-f1o 6550 df-fv 6551 df-ov 7415 df-er 8706 df-en 8943 df-dom 8944 df-sdom 8945 df-pnf 11255 df-mnf 11256 df-xr 11257 df-ltxr 11258 df-le 11259 df-2 12280
df-uhgr 28586 df-upgr 28610 df-umgr 28611 |
| This theorem is referenced by: umgredgprv
28635 umgr2edg
28734 subumgredg2
28810 subumgr
28813 umgrspan
28819 umgrreslem
28830 umgrres
28832 umgrres1lem
28835 vdumgr0
29005 vtxdumgr0nedg
29018 umgr2wlk
29471 umgrwwlks2on
29479 umgr3cyclex
29704 vdn0conngrumgrv2
29717 umgr2cycllem
34430 |
