Theorem exmo 2523

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 2503	. . 3 ⊢ (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
3	1, 2	sylibr 224	. 2 ⊢ (¬ ∃𝑥𝜑 → ∃*𝑥𝜑)
4	3	orri 390	1 ⊢ (∃𝑥𝜑 ∨ ∃*𝑥𝜑)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 382  ∃wex 1744  ∃!weu 2498  ∃*wmo 2499

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 384  df-mo 2503

This theorem is referenced by:  exmoeu  2531  moanim  2558  moexex  2570  mo2icl  3418  mosubopt  5001  dff3  6412  brdom3  9388  mof  32534