Theorem preq12i

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

	Ref	Expression
Hypotheses	preq1i.1	$$⊢A=B$$
	preq12i.2	$$⊢C=D$$
Assertion	preq12i	$$⊢\left\{A,C\right\}=\left\{B,D\right\}$$

Proof

Step	Hyp	Ref	Expression
1		preq1i.1	$$⊢A=B$$
2		preq12i.2	$$⊢C=D$$
3		preq12	$$⊢\left(A=B\wedge C=D\right)\to \left\{A,C\right\}=\left\{B,D\right\}$$
4	1 2 3	mp2an	$$⊢\left\{A,C\right\}=\left\{B,D\right\}$$