Theorem reubii

Description: Formula-building rule for restricted existential quantifier (inference form). (Contributed by NM, 22-Oct-1999)

	Ref	Expression
Hypothesis	reubii.1	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	reubii	⊢ ( ∃! 𝑥 ∈ 𝐴 𝜑 ↔ ∃! 𝑥 ∈ 𝐴 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		reubii.1	⊢ ( 𝜑 ↔ 𝜓 )
2	1	a1i	⊢ ( 𝑥 ∈ 𝐴 → ( 𝜑 ↔ 𝜓 ) )
3	2	reubiia	⊢ ( ∃! 𝑥 ∈ 𝐴 𝜑 ↔ ∃! 𝑥 ∈ 𝐴 𝜓 )