Theorem preq1d

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

	Ref	Expression
Hypothesis	preq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	preq1d	⊢ ( 𝜑 → { 𝐴 , 𝐶 } = { 𝐵 , 𝐶 } )

Proof

Step	Hyp	Ref	Expression
1		preq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		preq1	⊢ ( 𝐴 = 𝐵 → { 𝐴 , 𝐶 } = { 𝐵 , 𝐶 } )
3	1 2	syl	⊢ ( 𝜑 → { 𝐴 , 𝐶 } = { 𝐵 , 𝐶 } )