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Theorem relrpss 7165
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 7164 . 2 [] = {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
21relopabi 5444 1 Rel []
Colors of variables: wff setvar class
Syntax hints:  wpss 3767  Rel wrel 5313   [] crpss 7163
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1880  ax-4 1897  ax-5 2004  ax-6 2070  ax-7 2106  ax-9 2167  ax-10 2187  ax-11 2203  ax-12 2216  ax-13 2422  ax-ext 2784
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-3an 1102  df-tru 1641  df-ex 1860  df-nf 1865  df-sb 2063  df-clab 2792  df-cleq 2798  df-clel 2801  df-nfc 2936  df-rab 3104  df-v 3392  df-dif 3769  df-un 3771  df-in 3773  df-ss 3780  df-nul 4114  df-if 4277  df-sn 4368  df-pr 4370  df-op 4374  df-opab 4903  df-xp 5314  df-rel 5315  df-rpss 7164
This theorem is referenced by:  brrpssg  7166  compssiso  9478
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