Theorem ttceqd 36788

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

Hypothesis

Ref	Expression
ttceqd.1	⊢ (𝜑 → 𝐴 = 𝐵)

Assertion

Ref	Expression
ttceqd	⊢ (𝜑 → TC+ 𝐴 = TC+ 𝐵)

Proof of Theorem ttceqd

Step	Hyp	Ref	Expression
1		ttceqd.1	. 2 ⊢ (𝜑 → 𝐴 = 𝐵)
2		ttceq 36786	. 2 ⊢ (𝐴 = 𝐵 → TC+ 𝐴 = TC+ 𝐵)
3	1, 2	syl 17	1 ⊢ (𝜑 → TC+ 𝐴 = TC+ 𝐵)

Syntax hints:   → wi 4   = wceq 1550  TC+ cttc 36784

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1805  ax-4 1819  ax-5 1920  ax-6 1977  ax-7 2018  ax-8 2134  ax-9 2142  ax-ext 2724

This theorem depends on definitions:  df-bi 209  df-an 399  df-tru 1553  df-ex 1790  df-sb 2081  df-clab 2731  df-cleq 2744  df-clel 2827  df-rex 3077  df-v 3446  df-ss 3912  df-iun 4941  df-ttc 36785

This theorem is referenced by:  csbttc  36807