Theorem relmntop 33962

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 33961	. 2 ⊢ ManTop = {⟨𝑛, 𝑗⟩ ∣ (𝑛 ∈ ℕ0 ∧ (𝑗 ∈ 2ndω ∧ 𝑗 ∈ Haus ∧ 𝑗 ∈ Locally [(TopOpen‘(𝔼hil‘𝑛))] ≃ ))}
2	1	relopabiv 5839	1 ⊢ Rel ManTop

Syntax hints:   ∧ wa 395   ∧ w3a 1087   ∈ wcel 2108  Rel wrel 5700  ‘cfv 6568  [cec 8755  ℕ₀cn0 12547  TopOpenctopn 17475  Hauscha 23329  2^ndωc2ndc 23459  Locally clly 23485   ≃ chmph 23775  𝔼_hilcehl 25429  ManTopcmntop 33960

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-v 3490  df-ss 3993  df-opab 5229  df-xp 5701  df-rel 5702  df-mntop 33961

This theorem is referenced by: (None)