Theorem neufal 34595

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 34594	. 2 ⊢ ¬ ∃𝑥⊥
2		euex 2577	. 2 ⊢ (∃!𝑥⊥ → ∃𝑥⊥)
3	1, 2	mto 196	1 ⊢ ¬ ∃!𝑥⊥

Syntax hints:  ¬ wn 3  ⊥wfal 1551  ∃wex 1782  ∃!weu 2568

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-fal 1552  df-ex 1783  df-eu 2569

This theorem is referenced by:  unqsym1  34614