Theorem relmntop 34183

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 34182	. 2 ⊢ ManTop = {⟨𝑛, 𝑗⟩ ∣ (𝑛 ∈ ℕ0 ∧ (𝑗 ∈ 2ndω ∧ 𝑗 ∈ Haus ∧ 𝑗 ∈ Locally [(TopOpen‘(𝔼hil‘𝑛))] ≃ ))}
2	1	relopabiv 5770	1 ⊢ Rel ManTop

Syntax hints:   ∧ wa 395   ∧ w3a 1087   ∈ wcel 2114  Rel wrel 5630  ‘cfv 6493  [cec 8635  ℕ₀cn0 12405  TopOpenctopn 17345  Hauscha 23256  2^ndωc2ndc 23386  Locally clly 23412   ≃ chmph 23702  𝔼_hilcehl 25344  ManTopcmntop 34181

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 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3443  df-ss 3919  df-opab 5162  df-xp 5631  df-rel 5632  df-mntop 34182

This theorem is referenced by: (None)