Theorem preq1d

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

	Ref	Expression
Hypothesis	preq1d.1	$$⊢\phi \to A=B$$
Assertion	preq1d	$$⊢\phi \to \left\{A,C\right\}=\left\{B,C\right\}$$

Proof

Step	Hyp	Ref	Expression
1		preq1d.1	$$⊢\phi \to A=B$$
2		preq1	$$⊢A=B\to \left\{A,C\right\}=\left\{B,C\right\}$$
3	1 2	syl	$$⊢\phi \to \left\{A,C\right\}=\left\{B,C\right\}$$