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

Theorem relrpss 6515
 Description: The proper subset relation is a relation. (Contributed by Stefan O'Rear, 2-Nov-2014.)
Assertion
Ref Expression
relrpss []

Proof of Theorem relrpss
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-rpss 6514 . 2 []
21relopabi 4992 1 []
 Colors of variables: wff set class Syntax hints:   wpss 3313   wrel 4875   [] crpss 6513 This theorem is referenced by:  brrpssg  6516  compssiso  8246 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-opab 4259  df-xp 4876  df-rel 4877  df-rpss 6514
 Copyright terms: Public domain W3C validator