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Theorem dvdszrcl 14002
 Description: Reverse closure for the divisibility relation. (Contributed by Stefan O'Rear, 5-Sep-2015.)
Assertion
Ref Expression
dvdszrcl

Proof of Theorem dvdszrcl
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-dvds 13998 . . 3
2 opabssxp 5083 . . 3
31, 2eqsstri 3529 . 2
43brel 5057 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1395   wcel 1819  wrex 2808   class class class wbr 4456  copab 4514   cxp 5006  (class class class)co 6296   cmul 9514  cz 10885   cdvds 13997 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-sep 4578  ax-nul 4586  ax-pr 4695 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-br 4457  df-opab 4516  df-xp 5014  df-dvds 13998 This theorem is referenced by:  dvdsmulgcd  14203  oddvdsi  16698  odmulg  16704  gexdvdsi  16729  numclwwlk8  25241  nzss  31384  nzin  31385
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