Theorem unnf 31576

Description: There does not exist exactly one set, such that ⊥ is true. (Contributed by Anthony Hart, 13-Sep-2011.)

Assertion

Ref	Expression
unnf	⊢ ¬ ∃!𝑥⊥

Proof of Theorem unnf

Step	Hyp	Ref	Expression
1		nextf 31575	. 2 ⊢ ¬ ∃𝑥⊥
2		euex 2482	. 2 ⊢ (∃!𝑥⊥ → ∃𝑥⊥)
3	1, 2	mto 187	1 ⊢ ¬ ∃!𝑥⊥

Syntax hints:  ¬ wn 3  ⊥wfal 1480  ∃wex 1695  ∃!weu 2458

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875

This theorem depends on definitions:  df-bi 196  df-tru 1478  df-fal 1481  df-ex 1696  df-eu 2462

This theorem is referenced by:  unqsym1  31594