Theorem relrpss 7696

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 7695	. 2 ⊢ [⊊] = {⟨𝑥, 𝑦⟩ ∣ 𝑥 ⊊ 𝑦}
2	1	relopabiv 5786	1 ⊢ Rel [⊊]

Syntax hints:   ⊊ wpss 3900  Rel wrel 5645   [⊊] crpss 7694

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1809  ax-4 1823  ax-5 1924  ax-6 1981  ax-7 2022  ax-8 2138  ax-9 2146  ax-ext 2728

This theorem depends on definitions:  df-bi 209  df-an 399  df-tru 1557  df-ex 1794  df-sb 2085  df-clab 2735  df-cleq 2748  df-clel 2831  df-v 3450  df-ss 3916  df-opab 5157  df-xp 5646  df-rel 5647  df-rpss 7695

This theorem is referenced by:  brrpssg  7697  compssiso  10321