Theorem neufal 33756

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

Assertion

Ref	Expression
neufal	⊢ ¬ ∃!𝑥⊥

Proof of Theorem neufal

Step	Hyp	Ref	Expression
1		nexfal 33755	. 2 ⊢ ¬ ∃𝑥⊥
2		euex 2662	. 2 ⊢ (∃!𝑥⊥ → ∃𝑥⊥)
3	1, 2	mto 199	1 ⊢ ¬ ∃!𝑥⊥

Syntax hints:  ¬ wn 3  ⊥wfal 1549  ∃wex 1780  ∃!weu 2653

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796

This theorem depends on definitions:  df-bi 209  df-an 399  df-tru 1540  df-fal 1550  df-ex 1781  df-eu 2654

This theorem is referenced by:  unqsym1  33775