Mathbox for Steve Rodriguez < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  reldvds Structured version   Visualization version   Unicode version

Theorem reldvds 36675
 Description: The divides relation is in fact a relation. (Contributed by Steve Rodriguez, 20-Jan-2020.)
Assertion
Ref Expression
reldvds

Proof of Theorem reldvds
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-dvds 14318 . 2
21relopabi 4962 1
 Colors of variables: wff setvar class Syntax hints:   wa 371   wceq 1446   wcel 1889  wrex 2740   wrel 4842  (class class class)co 6295   cmul 9549  cz 10944   cdvds 14317 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-9 1898  ax-10 1917  ax-11 1922  ax-12 1935  ax-13 2093  ax-ext 2433  ax-sep 4528  ax-nul 4537  ax-pr 4642 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 988  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2583  df-ne 2626  df-ral 2744  df-rex 2745  df-rab 2748  df-v 3049  df-dif 3409  df-un 3411  df-in 3413  df-ss 3420  df-nul 3734  df-if 3884  df-sn 3971  df-pr 3973  df-op 3977  df-opab 4465  df-xp 4843  df-rel 4844  df-dvds 14318 This theorem is referenced by:  nznngen  36676  nzss  36677  nzin  36678  hashnzfz  36680
 Copyright terms: Public domain W3C validator