Theorem altopeq1

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

	Ref	Expression
Assertion	altopeq1	⊢ ( 𝐴 = 𝐵 → ⟪ 𝐴 , 𝐶 ⟫ = ⟪ 𝐵 , 𝐶 ⟫ )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ 𝐶 = 𝐶
2		altopeq12	⊢ ( ( 𝐴 = 𝐵 ∧ 𝐶 = 𝐶 ) → ⟪ 𝐴 , 𝐶 ⟫ = ⟪ 𝐵 , 𝐶 ⟫ )
3	1 2	mpan2	⊢ ( 𝐴 = 𝐵 → ⟪ 𝐴 , 𝐶 ⟫ = ⟪ 𝐵 , 𝐶 ⟫ )