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	⊢ ( 𝜑 → 𝐵 ∈ 𝐴 )
	riota5.2	⊢ ( ( 𝜑 ∧ 𝑥 ∈ 𝐴 ) → ( 𝜓 ↔ 𝑥 = 𝐵 ) )
Assertion	riota5	⊢ ( 𝜑 → ( ℩ 𝑥 ∈ 𝐴 𝜓 ) = 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		riota5.1	⊢ ( 𝜑 → 𝐵 ∈ 𝐴 )
2		riota5.2	⊢ ( ( 𝜑 ∧ 𝑥 ∈ 𝐴 ) → ( 𝜓 ↔ 𝑥 = 𝐵 ) )
3		nfcvd	⊢ ( 𝜑 → Ⅎ 𝑥 𝐵 )
4	3 1 2	riota5f	⊢ ( 𝜑 → ( ℩ 𝑥 ∈ 𝐴 𝜓 ) = 𝐵 )