Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > rusgrrgr | Structured version Visualization version GIF version |
Description: A k-regular simple graph is a k-regular graph. (Contributed by Alexander van der Vekens, 8-Jul-2018.) (Revised by AV, 18-Dec-2020.) |
Ref | Expression |
---|---|
rusgrrgr | ⊢ (𝐺 RegUSGraph 𝐾 → 𝐺 RegGraph 𝐾) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rusgrprop 27340 | . 2 ⊢ (𝐺 RegUSGraph 𝐾 → (𝐺 ∈ USGraph ∧ 𝐺 RegGraph 𝐾)) | |
2 | 1 | simprd 498 | 1 ⊢ (𝐺 RegUSGraph 𝐾 → 𝐺 RegGraph 𝐾) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2113 class class class wbr 5059 USGraphcusgr 26930 RegGraph crgr 27333 RegUSGraph crusgr 27334 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 ax-8 2115 ax-9 2123 ax-10 2144 ax-11 2160 ax-12 2176 ax-ext 2792 ax-sep 5196 ax-nul 5203 ax-pr 5323 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1084 df-tru 1539 df-ex 1780 df-nf 1784 df-sb 2069 df-mo 2621 df-eu 2653 df-clab 2799 df-cleq 2813 df-clel 2892 df-nfc 2962 df-ral 3142 df-rex 3143 df-rab 3146 df-v 3493 df-dif 3932 df-un 3934 df-in 3936 df-ss 3945 df-nul 4285 df-if 4461 df-sn 4561 df-pr 4563 df-op 4567 df-br 5060 df-opab 5122 df-xp 5554 df-rusgr 27336 |
This theorem is referenced by: 0grrgr 27358 rgrprc 27369 frrusgrord 28116 |
Copyright terms: Public domain | W3C validator |