Theorem neutru 35340

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

Assertion

Ref	Expression
neutru	⊢ ¬ ∃!𝑥⊤

Proof of Theorem neutru

Step	Hyp	Ref	Expression
1		nexntru 35337	. 2 ⊢ ¬ ∃𝑥 ¬ ⊤
2		eunex 5389	. 2 ⊢ (∃!𝑥⊤ → ∃𝑥 ¬ ⊤)
3	1, 2	mto 196	1 ⊢ ¬ ∃!𝑥⊤

Syntax hints:  ¬ wn 3  ⊤wtru 1543  ∃wex 1782  ∃!weu 2563

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-12 2172  ax-nul 5307  ax-pow 5364

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-nf 1787  df-mo 2535  df-eu 2564

This theorem is referenced by:  nmotru  35341