Theorem scott0 9879

Description: Applying Scott's trick to the empty set leaves it unchanged. (Contributed by BTernaryTau, 3-Jul-2026.)

Assertion

Ref	Expression
scott0	⊢ Scott ∅ = ∅

Proof of Theorem scott0

Step	Hyp	Ref	Expression
1		scottss 9878	. 2 ⊢ Scott ∅ ⊆ ∅
2		ss0 4355	. 2 ⊢ (Scott ∅ ⊆ ∅ → Scott ∅ = ∅)
3	1, 2	ax-mp 5	1 ⊢ Scott ∅ = ∅

This proof depends on syntax axioms:   = wceq 1570   ⊆ wss 3902  ∅c0 4282  Scott cscott 9871

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2741  df-cleq 2754  df-clel 2837  df-rab 3415  df-dif 3905  df-ss 3919  df-nul 4283  df-scott 9872

This theorem is used by:  scott0b  9880  kardval  35686