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Theorem relrpss 6459
Description: The proper subset relation is a relation. (Contributed by Stefan O'Rear, 2-Nov-2014.)
Assertion
Ref Expression
relrpss  |-  Rel [ C.]

Proof of Theorem relrpss
Dummy variables  x  y are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-rpss 6458 . 2  |- [ C.]  =  { <. x ,  y
>.  |  x  C.  y }
21relopabi 4940 1  |-  Rel [ C.]
Colors of variables: wff set class
Syntax hints:    C. wpss 3264   Rel wrel 4823   [ C.] crpss 6457
This theorem is referenced by:  brrpssg  6460  compssiso  8187
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368  ax-sep 4271  ax-nul 4279  ax-pr 4344
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-ne 2552  df-ral 2654  df-rex 2655  df-rab 2658  df-v 2901  df-dif 3266  df-un 3268  df-in 3270  df-ss 3277  df-nul 3572  df-if 3683  df-sn 3763  df-pr 3764  df-op 3766  df-opab 4208  df-xp 4824  df-rel 4825  df-rpss 6458
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