Theorem mof 32409

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

Assertion

Ref	Expression
mof	⊢ ∃*𝑥⊥

Proof of Theorem mof

Step	Hyp	Ref	Expression
1		nextf 32405	. 2 ⊢ ¬ ∃𝑥⊥
2		exmo 2495	. 2 ⊢ (∃𝑥⊥ ∨ ∃*𝑥⊥)
3	1, 2	mtpor 1695	1 ⊢ ∃*𝑥⊥

Syntax hints:  ⊥wfal 1488  ∃wex 1704  ∃*wmo 2471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722

This theorem depends on definitions:  df-bi 197  df-or 385  df-tru 1486  df-fal 1489  df-ex 1705  df-mo 2475

This theorem is referenced by:  amosym1  32425