Theorem relssr 38901

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 38899	. 2 ⊢ S = {⟨𝑥, 𝑦⟩ ∣ 𝑥 ⊆ 𝑦}
2	1	relopabiv 5776	1 ⊢ Rel S

Syntax hints:   ⊆ wss 3889  Rel wrel 5636   S cssr 38507

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3431  df-ss 3906  df-opab 5148  df-xp 5637  df-rel 5638  df-ssr 38899

This theorem is referenced by:  brssr  38902  issetssr  38904  brcnvssr  38907  extssr  38910