Theorem eubiOLD 40319

Description: Obsolete proof of eubi 2628 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 2120	. 2 ⊢ Ⅎ𝑥∀𝑥(𝜑 ↔ 𝜓)
2		sp 2145	. 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓))
3	1, 2	eubid 2632	1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃!𝑥𝜑 ↔ ∃!𝑥𝜓))

Syntax hints:   → wi 4   ↔ wb 207  ∀wal 1520  ∃!weu 2610

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1778  ax-4 1792  ax-5 1889  ax-6 1948  ax-7 1993  ax-10 2111  ax-12 2140

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-ex 1763  df-nf 1767  df-mo 2575  df-eu 2611

This theorem is referenced by: (None)