Theorem relrpss 7716

Description: The proper subset relation is a relation. (Contributed by Stefan O'Rear, 2-Nov-2014.)

Assertion

Ref	Expression
relrpss	⊢ Rel [⊊]

Proof of Theorem relrpss

Dummy variables 𝑥 𝑦 are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-rpss 7715	. 2 ⊢ [⊊] = {⟨𝑥, 𝑦⟩ ∣ 𝑥 ⊊ 𝑦}
2	1	relopabiv 5819	1 ⊢ Rel [⊊]

Syntax hints:   ⊊ wpss 3948  Rel wrel 5680   [⊊] crpss 7714

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1911  ax-6 1969  ax-7 2009  ax-8 2106  ax-9 2114  ax-ext 2701

This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1542  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2722  df-clel 2808  df-v 3474  df-in 3954  df-ss 3964  df-opab 5210  df-xp 5681  df-rel 5682  df-rpss 7715

This theorem is referenced by:  brrpssg  7717  compssiso  10371