Theorem s1eqd

Description: Equality theorem for a singleton word. (Contributed by Mario Carneiro, 26-Feb-2016)

	Ref	Expression
Hypothesis	s1eqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	s1eqd	⊢ ( 𝜑 → ⟨“ 𝐴 ”⟩ = ⟨“ 𝐵 ”⟩ )

Proof

Step	Hyp	Ref	Expression
1		s1eqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		s1eq	⊢ ( 𝐴 = 𝐵 → ⟨“ 𝐴 ”⟩ = ⟨“ 𝐵 ”⟩ )
3	1 2	syl	⊢ ( 𝜑 → ⟨“ 𝐴 ”⟩ = ⟨“ 𝐵 ”⟩ )