Theorem equvelv

Description: A biconditional form of equvel with disjoint variable conditions and proved from Tarski's FOL axiom schemes. (Contributed by Andrew Salmon, 2-Jun-2011) Reduce axiom usage. (Revised by Wolf Lammen, 10-Apr-2021) (Proof shortened by Wolf Lammen, 12-Jul-2022)

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

Proof

Step	Hyp	Ref	Expression
1		equequ1	$$⊢z=x\to \left(z=y\leftrightarrow x=y\right)$$
2	1	equsalvw	$$⊢\forall z\left(z=x\to z=y\right)\leftrightarrow x=y$$