Theorem unnt 31577

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

Assertion

Ref	Expression
unnt	⊢ ¬ ∃!𝑥⊤

Proof of Theorem unnt

Step	Hyp	Ref	Expression
1		nextnt 31574	. 2 ⊢ ¬ ∃𝑥 ¬ ⊤
2		eunex 4785	. 2 ⊢ (∃!𝑥⊤ → ∃𝑥 ¬ ⊤)
3	1, 2	mto 187	1 ⊢ ¬ ∃!𝑥⊤

Syntax hints:  ¬ wn 3  ⊤wtru 1476  ∃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  ax-7 1922  ax-8 1979  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-nul 4717  ax-pow 4769

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-eu 2462  df-mo 2463

This theorem is referenced by:  mont  31578