Theorem scotteqi 35509

Description: Equality theorem for the Scott operation. Inference form of scotteq 9860. (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 9860	. 2 ⊢ (𝐴 = 𝐵 → Scott 𝐴 = Scott 𝐵)
3	1, 2	ax-mp 5	1 ⊢ Scott 𝐴 = Scott 𝐵

Syntax hints:   = wceq 1570  Scott cscott 9853

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-ral 3080  df-rex 3090  df-rab 3417  df-scott 9854

This theorem is referenced by:  kard0  35567