Theorem eubiOLD 44405

Description: Obsolete proof of eubi 2587 as of 7-Oct-2022. (Contributed by Andrew Salmon, 11-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
eubiOLD	⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃!𝑥𝜑 ↔ ∃!𝑥𝜓))

Proof of Theorem eubiOLD

Step	Hyp	Ref	Expression
1		nfa1 2152	. 2 ⊢ Ⅎ𝑥∀𝑥(𝜑 ↔ 𝜓)
2		sp 2184	. 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓))
3	1, 2	eubid 2590	1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃!𝑥𝜑 ↔ ∃!𝑥𝜓))

Syntax hints:   → wi 4   ↔ wb 206  ∀wal 1535  ∃!weu 2571

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-10 2141  ax-12 2178

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-ex 1778  df-nf 1782  df-mo 2543  df-eu 2572

This theorem is referenced by: (None)