Theorem sneqd

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

	Ref	Expression
Hypothesis	sneqd.1	$$⊢\phi \to A=B$$
Assertion	sneqd	$$⊢\phi \to \left\{A\right\}=\left\{B\right\}$$

Proof

Step	Hyp	Ref	Expression
1		sneqd.1	$$⊢\phi \to A=B$$
2		sneq	$$⊢A=B\to \left\{A\right\}=\left\{B\right\}$$
3	1 2	syl	$$⊢\phi \to \left\{A\right\}=\left\{B\right\}$$