Theorem neutru 37410

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 37407	. 2 ⊢ ¬ ∃𝑥 ¬ ⊤
2		eunex 5359	. 2 ⊢ (∃!𝑥⊤ → ∃𝑥 ¬ ⊤)
3	1, 2	mto 200	1 ⊢ ¬ ∃!𝑥⊤

This proof depends on syntax axioms:  ¬ wn 3  ⊤wtru 1571  ∃wex 1812  ∃!weu 2596

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-10 2180  ax-12 2216  ax-nul 5266  ax-pow 5334

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-nf 1817  df-mo 2567  df-eu 2597

This theorem is used by:  nmotru  37411