Users' Mathboxes Mathbox for Peter Mazsa < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  dfdisjs Structured version   Visualization version   GIF version

Theorem dfdisjs 38689
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 38685 . 2 Disjs = ( Disjss ∩ Rels )
2 df-disjss 38684 . 2 Disjss = {𝑟 ∣ ≀ 𝑟 ∈ CnvRefRels }
31, 2abeqin 38233 1 Disjs = {𝑟 ∈ Rels ∣ ≀ 𝑟 ∈ CnvRefRels }
Colors of variables: wff setvar class
Syntax hints:   = wceq 1536  wcel 2105  {crab 3432  ccnv 5687  ccoss 38161   Rels crels 38163   CnvRefRels ccnvrefrels 38169   Disjss cdisjss 38193   Disjs cdisjs 38194
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1539  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-rab 3433  df-v 3479  df-in 3969  df-disjss 38684  df-disjs 38685
This theorem is referenced by:  dfdisjs2  38690  eldisjs  38703
  Copyright terms: Public domain W3C validator