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Theorem dvdszrcl 12862
 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 12858 . . 3
2 opabssxp 4953 . . 3
31, 2eqsstri 3380 . 2
43brel 4929 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726  wrex 2708   class class class wbr 4215  copab 4268   cxp 4879  (class class class)co 6084   cmul 9000  cz 10287   cdivides 12857 This theorem is referenced by:  dvdsmulgcd  13059  oddvdsi  15191  odmulg  15197  gexdvdsi  15222 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-opab 4270  df-xp 4887  df-dvds 12858
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