Theorem relssr 39555

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 39553	. 2 ⊢ S = {⟨𝑥, 𝑦⟩ ∣ 𝑥 ⊆ 𝑦}
2	1	relopabiv 5797	1 ⊢ Rel S

This proof depends on syntax axioms:   ⊆ wss 3895  Rel wrel 5655   S cssr 39161

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3896  df-opab 5167  df-xp 5656  df-rel 5657  df-ssr 39553

This theorem is used by:  brssr  39556  issetssr  39558  brcnvssr  39561  extssr  39564