Theorem mofal 32992

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 32988	. 2 ⊢ ¬ ∃𝑥⊥
2		exmo 2554	. 2 ⊢ (∃𝑥⊥ ∨ ∃*𝑥⊥)
3	1, 2	mtpor 1814	1 ⊢ ∃*𝑥⊥

Syntax hints:  ⊥wfal 1614  ∃wex 1823  ∃*wmo 2549

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021

This theorem depends on definitions:  df-bi 199  df-or 837  df-tru 1605  df-fal 1615  df-ex 1824  df-mo 2551

This theorem is referenced by:  amosym1  33008