Theorem exmo 2249

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		pm2.21 100	. . 3 ⊢ (¬ ∃xφ → (∃xφ → ∃!xφ))
2		df-mo 2209	. . 3 ⊢ (∃*xφ ↔ (∃xφ → ∃!xφ))
3	1, 2	sylibr 203	. 2 ⊢ (¬ ∃xφ → ∃*xφ)
4	3	orri 365	1 ⊢ (∃xφ ∨ ∃*xφ)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 357  ∃wex 1541  ∃!weu 2204  ∃*wmo 2205

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 177  df-or 359  df-mo 2209

This theorem is referenced by:  moexex  2273  mo2icl  3016  mosubopt  4613