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

Theorem relssr 37874
Description: The subset relation is a relation. (Contributed by Peter Mazsa, 1-Aug-2019.)
Assertion
Ref Expression
relssr Rel S

Proof of Theorem relssr
Dummy variables 𝑥 𝑦 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-ssr 37872 . 2 S = {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
21relopabiv 5811 1 Rel S
Colors of variables: wff setvar class
Syntax hints:  wss 3941  Rel wrel 5672   S cssr 37550
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 2695
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468  df-in 3948  df-ss 3958  df-opab 5202  df-xp 5673  df-rel 5674  df-ssr 37872
This theorem is referenced by:  brssr  37875  issetssr  37877  brcnvssr  37880  extssr  37883
  Copyright terms: Public domain W3C validator