Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 class class class wbr 5144
dom cdm 5673 –onto→wfo 6541 ‘cfv 6543 (class class class)co 7413
0cc0 11133 ..^cfzo 13654
♯chash 14316 iEdgciedg 28849 Trailsctrls 29543 EulerPathsceupth 30046 |
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 2166 ax-ext 2696 ax-sep 5295 ax-nul 5302 ax-pr 5424 |
This theorem depends on definitions:
df-bi 206 df-an 395
df-or 846 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2528 df-eu 2557 df-clab 2703 df-cleq 2717 df-clel 2802 df-nfc 2877 df-ne 2931 df-ral 3052 df-rex 3061 df-rab 3420 df-v 3465 df-sbc 3771 df-csb 3887 df-dif 3944 df-un 3946 df-in 3948 df-ss 3958 df-nul 4320 df-if 4526 df-sn 4626 df-pr 4628 df-op 4632 df-uni 4905 df-br 5145 df-opab 5207 df-mpt 5228 df-id 5571 df-xp 5679 df-rel 5680 df-cnv 5681 df-co 5682 df-dm 5683 df-rn 5684 df-res 5685 df-ima 5686 df-iota 6495 df-fun 6545 df-fn 6546 df-fo 6549 df-fv 6551 df-ov 7416 df-trls 29545 df-eupth 30047 |
This theorem is referenced by: eupthiswlk
30061 eupthres
30064 eupth2eucrct
30066 eupth2lem3
30085 |