Theorem preq1i

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

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

Proof

Step	Hyp	Ref	Expression
1		preq1i.1	$$⊢A=B$$
2		preq1	$$⊢A=B\to \left\{A,C\right\}=\left\{B,C\right\}$$
3	1 2	ax-mp	$$⊢\left\{A,C\right\}=\left\{B,C\right\}$$