Theorem eubiiOLD

Description: Obsolete version of eubii as of 27-Sep-2023. (Contributed by NM, 9-Jul-1994) (Revised by Mario Carneiro, 6-Oct-2016) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	eubii.1	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	eubiiOLD	⊢ ( ∃! 𝑥 𝜑 ↔ ∃! 𝑥 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		eubii.1	⊢ ( 𝜑 ↔ 𝜓 )
2		eubi	⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( ∃! 𝑥 𝜑 ↔ ∃! 𝑥 𝜓 ) )
3	2 1	mpg	⊢ ( ∃! 𝑥 𝜑 ↔ ∃! 𝑥 𝜓 )