Theorem preq1i

Description: Equality inference for unordered pairs. (Contributed by NM, 19-Oct-2012)

	Ref	Expression
Hypothesis	preq1i.1	⊢ 𝐴 = 𝐵
Assertion	preq1i	⊢ { 𝐴 , 𝐶 } = { 𝐵 , 𝐶 }

Proof

Step	Hyp	Ref	Expression
1		preq1i.1	⊢ 𝐴 = 𝐵
2		preq1	⊢ ( 𝐴 = 𝐵 → { 𝐴 , 𝐶 } = { 𝐵 , 𝐶 } )
3	1 2	ax-mp	⊢ { 𝐴 , 𝐶 } = { 𝐵 , 𝐶 }