Theorem relmntop 32835

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 32834	. 2 ⊢ ManTop = {⟨𝑛, 𝑗⟩ ∣ (𝑛 ∈ ℕ0 ∧ (𝑗 ∈ 2ndω ∧ 𝑗 ∈ Haus ∧ 𝑗 ∈ Locally [(TopOpen‘(𝔼hil‘𝑛))] ≃ ))}
2	1	relopabiv 5812	1 ⊢ Rel ManTop

Syntax hints:   ∧ wa 396   ∧ w3a 1087   ∈ wcel 2106  Rel wrel 5674  ‘cfv 6532  [cec 8684  ℕ₀cn0 12454  TopOpenctopn 17349  Hauscha 22741  2^ndωc2ndc 22871  Locally clly 22897   ≃ chmph 23187  𝔼_hilcehl 24830  ManTopcmntop 32833

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2702

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2709  df-cleq 2723  df-clel 2809  df-v 3475  df-in 3951  df-ss 3961  df-opab 5204  df-xp 5675  df-rel 5676  df-mntop 32834

This theorem is referenced by: (None)