MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  relrpss Structured version   Visualization version   GIF version

Theorem relrpss 7714
Description: The proper subset relation is a relation. (Contributed by Stefan O'Rear, 2-Nov-2014.)
Assertion
Ref Expression
relrpss Rel []

Proof of Theorem relrpss
Dummy variables 𝑥 𝑦 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-rpss 7713 . 2 [] = {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
21relopabiv 5821 1 Rel []
Colors of variables: wff setvar class
Syntax hints:  wpss 3950  Rel wrel 5682   [] crpss 7712
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-in 3956  df-ss 3966  df-opab 5212  df-xp 5683  df-rel 5684  df-rpss 7713
This theorem is referenced by:  brrpssg  7715  compssiso  10369
  Copyright terms: Public domain W3C validator