Theorem riota5

Description: A method for computing restricted iota. (Contributed by NM, 20-Oct-2011) (Revised by Mario Carneiro, 6-Dec-2016)

	Ref	Expression
Hypotheses	riota5.1	$$⊢\phi \to B\in A$$
	riota5.2	$$⊢\left(\phi \wedge x\in A\right)\to \left(\psi \leftrightarrow x=B\right)$$
Assertion	riota5	$$⊢\phi \to \left(\iota x\in A|\psi \right)=B$$

Proof

Step	Hyp	Ref	Expression
1		riota5.1	$$⊢\phi \to B\in A$$
2		riota5.2	$$⊢\left(\phi \wedge x\in A\right)\to \left(\psi \leftrightarrow x=B\right)$$
3		nfcvd	$$⊢\phi \to \underset{\_}{Ⅎ}xB$$
4	3 1 2	riota5f	$$⊢\phi \to \left(\iota x\in A|\psi \right)=B$$