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Metamath Proof Explorer

Theorem equequ2

Description: An equivalence law for equality. (Contributed by NM, 21-Jun-1993) (Proof shortened by Wolf Lammen, 4-Aug-2017) (Proof shortened by BJ, 12-Apr-2021)

		Ref	Expression
	Assertion	equequ2	$⊢ x = y \to (z = x \leftrightarrow z = y)$

Proof

Step	Hyp	Ref	Expression
1		equtrr	$⊢ x = y \to (z = x \to z = y)$
2		equeuclr	$⊢ x = y \to (z = y \to z = x)$
3	1 2	impbid	$⊢ x = y \to (z = x \leftrightarrow z = y)$