Theorem scott0 9939

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 9938	. 2 ⊢ Scott ∅ ⊆ ∅
2		ss0 4351	. 2 ⊢ (Scott ∅ ⊆ ∅ → Scott ∅ = ∅)
3	1, 2	ax-mp 5	1 ⊢ Scott ∅ = ∅

This proof depends on syntax axioms:   = wceq 1569   ⊆ wss 3895  ∅c0 4278  Scott cscott 9931

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-rab 3413  df-ss 3896  df-dif 4047  df-nul 4279  df-scott 9932

This theorem is used by:  scott0b  9940  kardval  35876