Theorem exmo 2495

Description: Something exists or at most one exists. (Contributed by NM, 8-Mar-1995.)

Assertion

Ref	Expression
exmo	⊢ (∃𝑥𝜑 ∨ ∃*𝑥𝜑)

Proof of Theorem exmo

Step	Hyp	Ref	Expression
1		pm2.21 120	. . 3 ⊢ (¬ ∃𝑥𝜑 → (∃𝑥𝜑 → ∃!𝑥𝜑))
2		df-mo 2475	. . 3 ⊢ (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
3	1, 2	sylibr 224	. 2 ⊢ (¬ ∃𝑥𝜑 → ∃*𝑥𝜑)
4	3	orri 391	1 ⊢ (∃𝑥𝜑 ∨ ∃*𝑥𝜑)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 383  ∃wex 1704  ∃!weu 2470  ∃*wmo 2471

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

This theorem depends on definitions:  df-bi 197  df-or 385  df-mo 2475

This theorem is referenced by:  exmoeu  2502  moanim  2529  moexex  2541  mo2icl  3385  mosubopt  4972  dff3  6372  brdom3  9350  mof  32409