Theorem exmo 2540

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 2567. (Revised by BJ, 14-Oct-2022.)

Assertion

Ref	Expression
exmo	⊢ (∃𝑥𝜑 ∨ ∃*𝑥𝜑)

Proof of Theorem exmo

Step	Hyp	Ref	Expression
1		nexmo 2539	. 2 ⊢ (¬ ∃𝑥𝜑 → ∃*𝑥𝜑)
2	1	orri 862	1 ⊢ (∃𝑥𝜑 ∨ ∃*𝑥𝜑)

Syntax hints:   ∨ wo 847  ∃wex 1776  ∃*wmo 2536

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965

This theorem depends on definitions:  df-bi 207  df-or 848  df-ex 1777  df-mo 2538

This theorem is referenced by:  brdom3  10566  mofal  36392