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Theorem relssr 35185
 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 35183 . 2 S = {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
21relopabi 5538 1 Rel S
 Colors of variables: wff setvar class Syntax hints:   ⊆ wss 3823  Rel wrel 5406   S cssr 34900 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-ext 2744 This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-3an 1070  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-clab 2753  df-cleq 2765  df-clel 2840  df-nfc 2912  df-rab 3091  df-v 3411  df-dif 3826  df-un 3828  df-in 3830  df-ss 3837  df-nul 4173  df-if 4345  df-sn 4436  df-pr 4438  df-op 4442  df-opab 4986  df-xp 5407  df-rel 5408  df-ssr 35183 This theorem is referenced by:  brssr  35186  issetssr  35188  brcnvssr  35191  extssr  35194
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