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Metamath Proof Explorer

Theorem preq2d

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

		Ref	Expression
	Hypothesis	preq1d.1	$⊢ φ \to A = B$
	Assertion	preq2d	$⊢ φ \to \{C, A\} = \{C, B\}$

Step	Hyp	Ref	Expression
1		preq1d.1	$⊢ φ \to A = B$
2		preq2	$⊢ A = B \to \{C, A\} = \{C, B\}$
3	1 2	syl	$⊢ φ \to \{C, A\} = \{C, B\}$