Theorem equequ1

Description: An equivalence law for equality. (Contributed by NM, 1-Aug-1993) (Proof shortened by Wolf Lammen, 10-Dec-2017)

	Ref	Expression
Assertion	equequ1	$$⊢x=y\to \left(x=z\leftrightarrow y=z\right)$$

Proof

Step	Hyp	Ref	Expression
1		ax7	$$⊢x=y\to \left(x=z\to y=z\right)$$
2		equtr	$$⊢x=y\to \left(y=z\to x=z\right)$$
3	1 2	impbid	$$⊢x=y\to \left(x=z\leftrightarrow y=z\right)$$