Theorem sneqd

Description: Equality deduction for singletons. (Contributed by NM, 22-Jan-2004)

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

Proof

Step	Hyp	Ref	Expression
1		sneqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		sneq	⊢ ( 𝐴 = 𝐵 → { 𝐴 } = { 𝐵 } )
3	1 2	syl	⊢ ( 𝜑 → { 𝐴 } = { 𝐵 } )