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Theorem sscrel 17822
Description: The subcategory subset relation is a relation. (Contributed by Mario Carneiro, 6-Jan-2017.)
Assertion
Ref Expression
sscrel Rel ⊆cat

Proof of Theorem sscrel
Dummy variables 𝑗 𝑠 𝑡 𝑥 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-ssc 17819 . 2 cat = {⟨, 𝑗⟩ ∣ ∃𝑡(𝑗 Fn (𝑡 × 𝑡) ∧ ∃𝑠 ∈ 𝒫 𝑡X𝑥 ∈ (𝑠 × 𝑠)𝒫 (𝑗𝑥))}
21relopabiv 5817 1 Rel ⊆cat
Colors of variables: wff setvar class
Syntax hints:  wa 394  wex 1774  wcel 2099  wrex 3060  𝒫 cpw 4598   × cxp 5671  Rel wrel 5678   Fn wfn 6539  cfv 6544  Xcixp 8916  cat cssc 17816
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2704  df-cleq 2718  df-clel 2803  df-v 3465  df-ss 3964  df-opab 5207  df-xp 5679  df-rel 5680  df-ssc 17819
This theorem is referenced by:  brssc  17823  ssc1  17830  ssc2  17831  ssctr  17834  issubc  17847
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