Theorem scotteqi 35569

Description: Equality theorem for the Scott operation. Inference form of scotteq 9867. (Contributed by BTernaryTau, 3-Jul-2026.)

Hypothesis

Ref	Expression
scotteqi.1	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
scotteqi	⊢ Scott 𝐴 = Scott 𝐵

Proof of Theorem scotteqi

Step	Hyp	Ref	Expression
1		scotteqi.1	. 2 ⊢ 𝐴 = 𝐵
2		scotteq 9867	. 2 ⊢ (𝐴 = 𝐵 → Scott 𝐴 = Scott 𝐵)
3	1, 2	ax-mp 5	1 ⊢ Scott 𝐴 = Scott 𝐵

This proof depends on syntax axioms:   = wceq 1570  Scott cscott 9864

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 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-ral 3082  df-rex 3092  df-rab 3419  df-scott 9865

This theorem is used by:  kard0  35626