Theorem preq2i

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

	Ref	Expression
Hypothesis	preq1i.1	$$⊢A=B$$
Assertion	preq2i	$$⊢\left\{C,A\right\}=\left\{C,B\right\}$$

Proof

Step	Hyp	Ref	Expression
1		preq1i.1	$$⊢A=B$$
2		preq2	$$⊢A=B\to \left\{C,A\right\}=\left\{C,B\right\}$$
3	1 2	ax-mp	$$⊢\left\{C,A\right\}=\left\{C,B\right\}$$