Theorem ttceqd

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

	Ref	Expression
Hypothesis	ttceqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	ttceqd	⊢ ( 𝜑 → TC+ 𝐴 = TC+ 𝐵 )

Proof

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