Theorem neutru 36389

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 36386	. 2 ⊢ ¬ ∃𝑥 ¬ ⊤
2		eunex 5395	. 2 ⊢ (∃!𝑥⊤ → ∃𝑥 ¬ ⊤)
3	1, 2	mto 197	1 ⊢ ¬ ∃!𝑥⊤

Syntax hints:  ¬ wn 3  ⊤wtru 1537  ∃wex 1775  ∃!weu 2565

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-10 2138  ax-12 2174  ax-nul 5311  ax-pow 5370

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1539  df-ex 1776  df-nf 1780  df-mo 2537  df-eu 2566

This theorem is referenced by:  nmotru  36390