Theorem scott0i 35453

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

Assertion

Ref	Expression
scott0i	⊢ Scott ∅ = ∅

Proof of Theorem scott0i

Step	Hyp	Ref	Expression
1		scottss 9869	. 2 ⊢ Scott ∅ ⊆ ∅
2		ss0 4366	. 2 ⊢ (Scott ∅ ⊆ ∅ → Scott ∅ = ∅)
3	1, 2	ax-mp 5	1 ⊢ Scott ∅ = ∅

Syntax hints:   = wceq 1567   ⊆ wss 3913  ∅c0 4294  Scott cscott 9857

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1570  df-fal 1580  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-rab 3424  df-dif 3916  df-ss 3930  df-nul 4295  df-scott 9858

This theorem is referenced by:  kardval  35498