Theorem ttceqd 36678

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 36676	. 2 ⊢ (𝐴 = 𝐵 → TC+ 𝐴 = TC+ 𝐵)
3	1, 2	syl 17	1 ⊢ (𝜑 → TC+ 𝐴 = TC+ 𝐵)

Syntax hints:   → wi 4   = wceq 1542  TC+ cttc 36674

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rex 3063  df-v 3432  df-ss 3907  df-iun 4936  df-ttc 36675

This theorem is referenced by:  csbttc  36697