Theorem relrpss 7729

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 7728	. 2 ⊢ [⊊] = {⟨𝑥, 𝑦⟩ ∣ 𝑥 ⊊ 𝑦}
2	1	relopabiv 5798	1 ⊢ Rel [⊊]

This proof depends on syntax axioms:   ⊊ wpss 3900  Rel wrel 5656   [⊊] crpss 7727

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2733

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2740  df-cleq 2753  df-clel 2836  df-v 3453  df-ss 3916  df-opab 5168  df-xp 5657  df-rel 5658  df-rpss 7728

This theorem is used by:  brrpssg  7730  compssiso  10433