Theorem eqeq1i

Description: Inference from equality to equivalence of equalities. (Contributed by NM, 15-Jul-1993)

	Ref	Expression
Hypothesis	eqeq1i.1	⊢ 𝐴 = 𝐵
Assertion	eqeq1i	⊢ ( 𝐴 = 𝐶 ↔ 𝐵 = 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		eqeq1i.1	⊢ 𝐴 = 𝐵
2		eqeq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 = 𝐶 ↔ 𝐵 = 𝐶 ) )
3	1 2	ax-mp	⊢ ( 𝐴 = 𝐶 ↔ 𝐵 = 𝐶 )