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	|- ( ph -> B e. A )
	riota5.2	|- ( ( ph /\ x e. A ) -> ( ps <-> x = B ) )
Assertion	riota5	|- ( ph -> ( iota_ x e. A ps ) = B )

Proof

Step	Hyp	Ref	Expression
1		riota5.1	|- ( ph -> B e. A )
2		riota5.2	|- ( ( ph /\ x e. A ) -> ( ps <-> x = B ) )
3		nfcvd	|- ( ph -> F/_ x B )
4	3 1 2	riota5f	|- ( ph -> ( iota_ x e. A ps ) = B )