Theorem preq12

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

	Ref	Expression
Assertion	preq12	$$⊢\left(A=C\wedge B=D\right)\to \left\{A,B\right\}=\left\{C,D\right\}$$

Proof

Step	Hyp	Ref	Expression
1		preq1	$$⊢A=C\to \left\{A,B\right\}=\left\{C,B\right\}$$
2		preq2	$$⊢B=D\to \left\{C,B\right\}=\left\{C,D\right\}$$
3	1 2	sylan9eq	$$⊢\left(A=C\wedge B=D\right)\to \left\{A,B\right\}=\left\{C,D\right\}$$