Theorem eubiiOLD 2606

Description: Obsolete version of eubii 2605 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.)

Hypothesis

Ref	Expression
eubii.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
eubiiOLD	⊢ (∃!𝑥𝜑 ↔ ∃!𝑥𝜓)

Proof of Theorem eubiiOLD

Step	Hyp	Ref	Expression
1		eubi 2604	. 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃!𝑥𝜑 ↔ ∃!𝑥𝜓))
2		eubii.1	. 2 ⊢ (𝜑 ↔ 𝜓)
3	1, 2	mpg 1800	1 ⊢ (∃!𝑥𝜑 ↔ ∃!𝑥𝜓)

Syntax hints:   ↔ wb 209  ∃!weu 2588

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1783  df-mo 2558  df-eu 2589

This theorem is referenced by: (None)