Theorem iotaequ

Description: Theorem *14.2 in WhiteheadRussell p. 189. (Contributed by Andrew Salmon, 11-Jul-2011)

	Ref	Expression
Assertion	iotaequ	$$⊢\left(\iota x|x=y\right)=y$$

Proof

Step	Hyp	Ref	Expression
1		iotaval	$$⊢\forall x\left(x=y\leftrightarrow x=y\right)\to \left(\iota x|x=y\right)=y$$
2		biid	$$⊢x=y\leftrightarrow x=y$$
3	1 2	mpg	$$⊢\left(\iota x|x=y\right)=y$$