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Theorem dfdisjs 36381
 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 36377 . 2 Disjs = ( Disjss ∩ Rels )
2 df-disjss 36376 . 2 Disjss = {𝑟 ∣ ≀ 𝑟 ∈ CnvRefRels }
31, 2abeqin 35954 1 Disjs = {𝑟 ∈ Rels ∣ ≀ 𝑟 ∈ CnvRefRels }
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538   ∈ wcel 2111  {crab 3074  ◡ccnv 5523   ≀ ccoss 35893   Rels crels 35895   CnvRefRels ccnvrefrels 35901   Disjss cdisjss 35925   Disjs cdisjs 35926 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2729 This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2736  df-cleq 2750  df-clel 2830  df-rab 3079  df-v 3411  df-in 3865  df-disjss 36376  df-disjs 36377 This theorem is referenced by:  dfdisjs2  36382  eldisjs  36395
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