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Theorem dfdisjs 38212
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 38208 . 2 Disjs = ( Disjss ∩ Rels )
2 df-disjss 38207 . 2 Disjss = {𝑟 ∣ ≀ 𝑟 ∈ CnvRefRels }
31, 2abeqin 37756 1 Disjs = {𝑟 ∈ Rels ∣ ≀ 𝑟 ∈ CnvRefRels }
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  wcel 2098  {crab 3430  ccnv 5681  ccoss 37681   Rels crels 37683   CnvRefRels ccnvrefrels 37689   Disjss cdisjss 37713   Disjs cdisjs 37714
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2706  df-cleq 2720  df-clel 2806  df-rab 3431  df-v 3475  df-in 3956  df-disjss 38207  df-disjs 38208
This theorem is referenced by:  dfdisjs2  38213  eldisjs  38226
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