Theorem relmntop 29396

Description: Manifold is a relation. (Contributed by Thierry Arnoux, 28-Dec-2019.)

Assertion

Ref	Expression
relmntop	⊢ Rel ManTop

Proof of Theorem relmntop

Dummy variables 𝑗 𝑛 are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-mntop 29395	. 2 ⊢ ManTop = {⟨𝑛, 𝑗⟩ ∣ (𝑛 ∈ ℕ0 ∧ (𝑗 ∈ 2nd𝜔 ∧ 𝑗 ∈ Haus ∧ 𝑗 ∈ Locally [(TopOpen‘(𝔼hil‘𝑛))] ≃ ))}
2	1	relopabi 5167	1 ⊢ Rel ManTop

Syntax hints:   ∧ wa 383   ∧ w3a 1031   ∈ wcel 1977  Rel wrel 5043  ‘cfv 5804  [cec 7627  ℕ₀cn0 11169  TopOpenctopn 15905  Hauscha 20922  2^nd𝜔c2ndc 21051  Locally clly 21077   ≃ chmph 21367  𝔼_hilcehl 22980  ManTopcmntop 29394

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-opab 4644  df-xp 5044  df-rel 5045  df-mntop 29395

This theorem is referenced by: (None)