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

Theorem disjALTVinidres 38166
Description: The intersection with restricted identity relation is disjoint. (Contributed by Peter Mazsa, 31-Dec-2021.)
Assertion
Ref Expression
disjALTVinidres Disj (𝑅 ∩ ( I ↾ 𝐴))

Proof of Theorem disjALTVinidres
StepHypRef Expression
1 disjALTVid 38164 . 2 Disj I
2 disjiminres 38161 . 2 ( Disj I → Disj (𝑅 ∩ ( I ↾ 𝐴)))
31, 2ax-mp 5 1 Disj (𝑅 ∩ ( I ↾ 𝐴))
Colors of variables: wff setvar class
Syntax hints:  cin 3943   I cid 5569  cres 5674   Disj wdisjALTV 37617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-11 2147  ax-12 2164  ax-ext 2698  ax-sep 5293  ax-nul 5300  ax-pr 5423
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-nf 1779  df-sb 2061  df-clab 2705  df-cleq 2719  df-clel 2805  df-ral 3057  df-rex 3066  df-rab 3428  df-v 3471  df-dif 3947  df-un 3949  df-in 3951  df-ss 3961  df-nul 4319  df-if 4525  df-sn 4625  df-pr 4627  df-op 4631  df-br 5143  df-opab 5205  df-id 5570  df-xp 5678  df-rel 5679  df-cnv 5680  df-co 5681  df-dm 5682  df-rn 5683  df-res 5684  df-coss 37820  df-cnvrefrel 37936  df-funALTV 38091  df-disjALTV 38114
This theorem is referenced by:  eqvrel1cossinidres  38200  detinidres  38205  petinidres2  38229
  Copyright terms: Public domain W3C validator