Theorem relssr 37972

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.

Step	Hyp	Ref	Expression
1		df-ssr 37970	. 2 ⊢ S = {⟨𝑥, 𝑦⟩ ∣ 𝑥 ⊆ 𝑦}
2	1	relopabiv 5822	1 ⊢ Rel S

Syntax hints:   ⊆ wss 3947  Rel wrel 5683   S cssr 37651

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 2699

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3473  df-in 3954  df-ss 3964  df-opab 5211  df-xp 5684  df-rel 5685  df-ssr 37970

This theorem is referenced by:  brssr  37973  issetssr  37975  brcnvssr  37978  extssr  37981