Theorem ttceqd 37096

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 37094	. 2 ⊢ (𝐴 = 𝐵 → TC+ 𝐴 = TC+ 𝐵)
3	1, 2	syl 18	1 ⊢ (𝜑 → TC+ 𝐴 = TC+ 𝐵)

This proof depends on syntax axioms:   → wi 4   = wceq 1570  TC+ cttc 37092

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2741  df-cleq 2754  df-clel 2837  df-rex 3089  df-v 3455  df-ss 3919  df-iun 4956  df-ttc 37093

This theorem is used by:  csbttc  37115