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Theorem dfdisjs 35472
 Description: Alternate definition of the class of disjoints. (Contributed by Peter Mazsa, 18-Jul-2021.)
Assertion
Ref Expression
dfdisjs Disjs = {𝑟 ∈ Rels ∣ ≀ 𝑟 ∈ CnvRefRels }

Proof of Theorem dfdisjs
StepHypRef Expression
1 df-disjs 35468 . 2 Disjs = ( Disjss ∩ Rels )
2 df-disjss 35467 . 2 Disjss = {𝑟 ∣ ≀ 𝑟 ∈ CnvRefRels }
31, 2abeqin 35046 1 Disjs = {𝑟 ∈ Rels ∣ ≀ 𝑟 ∈ CnvRefRels }
 Colors of variables: wff setvar class Syntax hints:   = wceq 1522   ∈ wcel 2081  {crab 3109  ◡ccnv 5442   ≀ ccoss 34985   Rels crels 34987   CnvRefRels ccnvrefrels 34993   Disjss cdisjss 35017   Disjs cdisjs 35018 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992  ax-8 2083  ax-9 2091  ax-10 2112  ax-11 2126  ax-12 2141  ax-ext 2769 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-tru 1525  df-ex 1762  df-nf 1766  df-sb 2043  df-clab 2776  df-cleq 2788  df-clel 2863  df-nfc 2935  df-rab 3114  df-v 3439  df-in 3866  df-disjss 35467  df-disjs 35468 This theorem is referenced by:  dfdisjs2  35473  eldisjs  35486
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