Theorem euanvOLD 2714

Description: Obsolete version of euanv 2713 as of 14-Jan-2023. (Contributed by NM, 23-Mar-1995.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
euanvOLD	⊢ (∃!𝑥(𝜑 ∧ 𝜓) ↔ (𝜑 ∧ ∃!𝑥𝜓))

Distinct variable group:   𝜑,𝑥

Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem euanvOLD

Step	Hyp	Ref	Expression
1		nfv 2013	. 2 ⊢ Ⅎ𝑥𝜑
2	1	euan 2709	1 ⊢ (∃!𝑥(𝜑 ∧ 𝜓) ↔ (𝜑 ∧ ∃!𝑥𝜓))

Syntax hints:   ↔ wb 198   ∧ wa 386  ∃!weu 2639

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-12 2220

This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1879  df-nf 1883  df-mo 2605  df-eu 2640

This theorem is referenced by: (None)