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 875	1 ⊢ (∃𝑥𝜑 ∨ ∃*𝑥𝜑)

Syntax hints:   ∨ wo 860  ∃wex 1809  ∃*wmo 2565

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-ex 1810  df-mo 2567

This theorem is referenced by:  brdom3  10507  mofal  36920