Theorem scotteqi 35450

Description: Equality theorem for the Scott operation. Inference form of scotteq 9864. (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 9864	. 2 ⊢ (𝐴 = 𝐵 → Scott 𝐴 = Scott 𝐵)
3	1, 2	ax-mp 5	1 ⊢ Scott 𝐴 = Scott 𝐵

Syntax hints:   = wceq 1567  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-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-ral 3086  df-rex 3096  df-rab 3424  df-scott 9858

This theorem is referenced by:  kard0  35500