Theorem relmntop 33948

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 33947	. 2 ⊢ ManTop = {⟨𝑛, 𝑗⟩ ∣ (𝑛 ∈ ℕ0 ∧ (𝑗 ∈ 2ndω ∧ 𝑗 ∈ Haus ∧ 𝑗 ∈ Locally [(TopOpen‘(𝔼hil‘𝑛))] ≃ ))}
2	1	relopabiv 5828	1 ⊢ Rel ManTop

Syntax hints:   ∧ wa 395   ∧ w3a 1085   ∈ wcel 2104  Rel wrel 5689  ‘cfv 6559  [cec 8737  ℕ₀cn0 12518  TopOpenctopn 17458  Hauscha 23314  2^ndωc2ndc 23444  Locally clly 23470   ≃ chmph 23760  𝔼_hilcehl 25414  ManTopcmntop 33946

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1963  ax-7 2003  ax-8 2106  ax-9 2114  ax-ext 2704

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1538  df-ex 1775  df-sb 2061  df-clab 2711  df-cleq 2725  df-clel 2812  df-v 3479  df-ss 3980  df-opab 5213  df-xp 5690  df-rel 5691  df-mntop 33947

This theorem is referenced by: (None)