Theorem relrpss 7555

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 7554	. 2 ⊢ [⊊] = {⟨𝑥, 𝑦⟩ ∣ 𝑥 ⊊ 𝑦}
2	1	relopabiv 5719	1 ⊢ Rel [⊊]

Syntax hints:   ⊊ wpss 3884  Rel wrel 5585   [⊊] crpss 7553

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-in 3890  df-ss 3900  df-opab 5133  df-xp 5586  df-rel 5587  df-rpss 7554

This theorem is referenced by:  brrpssg  7556  compssiso  10061