Theorem altopeq2

Description: Equality for alternate ordered pairs. (Contributed by Scott Fenton, 22-Mar-2012)

	Ref	Expression
Assertion	altopeq2	⊢ ( 𝐴 = 𝐵 → ⟪ 𝐶 , 𝐴 ⟫ = ⟪ 𝐶 , 𝐵 ⟫ )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ 𝐶 = 𝐶
2		altopeq12	⊢ ( ( 𝐶 = 𝐶 ∧ 𝐴 = 𝐵 ) → ⟪ 𝐶 , 𝐴 ⟫ = ⟪ 𝐶 , 𝐵 ⟫ )
3	1 2	mpan	⊢ ( 𝐴 = 𝐵 → ⟪ 𝐶 , 𝐴 ⟫ = ⟪ 𝐶 , 𝐵 ⟫ )