Theorem relrpss 7711

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 7710	. 2 ⊢ [⊊] = {⟨𝑥, 𝑦⟩ ∣ 𝑥 ⊊ 𝑦}
2	1	relopabiv 5798	1 ⊢ Rel [⊊]

Syntax hints:   ⊊ wpss 3908  Rel wrel 5657   [⊊] crpss 7709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-8 2147  ax-9 2155  ax-ext 2737

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1566  df-ex 1803  df-sb 2094  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-ss 3924  df-opab 5168  df-xp 5658  df-rel 5659  df-rpss 7710

This theorem is referenced by:  brrpssg  7712  compssiso  10346