Theorem mofal 34525

Description: There exist at most one set such that ⊥ is true. (Contributed by Anthony Hart, 13-Sep-2011.)

Assertion

Ref	Expression
mofal	⊢ ∃*𝑥⊥

Proof of Theorem mofal

Step	Hyp	Ref	Expression
1		nexfal 34521	. 2 ⊢ ¬ ∃𝑥⊥
2		exmo 2542	. 2 ⊢ (∃𝑥⊥ ∨ ∃*𝑥⊥)
3	1, 2	mtpor 1774	1 ⊢ ∃*𝑥⊥

Syntax hints:  ⊥wfal 1551  ∃wex 1783  ∃*wmo 2538

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972

This theorem depends on definitions:  df-bi 206  df-or 844  df-tru 1542  df-fal 1552  df-ex 1784  df-mo 2540

This theorem is referenced by:  nrmo  34526  amosym1  34542