Theorem exmo 2570

Description: Any proposition holds for some 𝑥 or holds for at most one 𝑥. (Contributed by NM, 8-Mar-1995.) Shorten proof and avoid df-eu 2597. (Revised by BJ, 14-Oct-2022.)

Assertion

Ref	Expression
exmo	⊢ (∃𝑥𝜑 ∨ ∃*𝑥𝜑)

Proof of Theorem exmo

Step	Hyp	Ref	Expression
1		nexmo 2569	. 2 ⊢ (¬ ∃𝑥𝜑 → ∃*𝑥𝜑)
2	1	orri 876	1 ⊢ (∃𝑥𝜑 ∨ ∃*𝑥𝜑)

This proof depends on syntax axioms:   ∨ wo 861  ∃wex 1811  ∃*wmo 2565

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-ex 1812  df-mo 2567

This theorem is used by:  brdom3  10620  mofal  37330