Theorem neutru 36635

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 36632	. 2 ⊢ ¬ ∃𝑥 ¬ ⊤
2		eunex 5319	. 2 ⊢ (∃!𝑥⊤ → ∃𝑥 ¬ ⊤)
3	1, 2	mto 198	1 ⊢ ¬ ∃!𝑥⊤

Syntax hints:  ¬ wn 3  ⊤wtru 1548  ∃wex 1786  ∃!weu 2572

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-10 2152  ax-12 2189  ax-nul 5228  ax-pow 5294

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-tru 1550  df-ex 1787  df-nf 1791  df-mo 2543  df-eu 2573

This theorem is referenced by:  nmotru  36636