Theorem ttceqi 36944

Description: Equality inference for transitive closure. (Contributed by Matthew House, 6-Apr-2026.)

Hypothesis

Ref	Expression
ttceqi.1	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
ttceqi	⊢ TC+ 𝐴 = TC+ 𝐵

Proof of Theorem ttceqi

Step	Hyp	Ref	Expression
1		ttceqi.1	. 2 ⊢ 𝐴 = 𝐵
2		ttceq 36943	. 2 ⊢ (𝐴 = 𝐵 → TC+ 𝐴 = TC+ 𝐵)
3	1, 2	ax-mp 5	1 ⊢ TC+ 𝐴 = TC+ 𝐵

Syntax hints:   = wceq 1568  TC+ cttc 36941

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2143  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1571  df-ex 1808  df-sb 2095  df-clab 2740  df-cleq 2753  df-clel 2836  df-rex 3088  df-v 3455  df-ss 3921  df-iun 4957  df-ttc 36942

This theorem is referenced by: (None)