Theorem relssr 38753

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 38751	. 2 ⊢ S = {⟨𝑥, 𝑦⟩ ∣ 𝑥 ⊆ 𝑦}
2	1	relopabiv 5769	1 ⊢ Rel S

Syntax hints:   ⊆ wss 3901  Rel wrel 5629   S cssr 38386

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3442  df-ss 3918  df-opab 5161  df-xp 5630  df-rel 5631  df-ssr 38751

This theorem is referenced by:  brssr  38754  issetssr  38756  brcnvssr  38759  extssr  38762