Theorem exmo 1042

Description: Something exists or at most one exists.

Assertion

Ref	Expression
exmo	⊢ (∃xφ ∨ ∃*xφ)

Proof of Theorem exmo

Step	Hyp	Ref	Expression
1		pm2.21 71	. . 3 ⊢ (¬ ∃xφ → (∃xφ → ∃!xφ))
2		df-mo 1010	. . 3 ⊢ (∃*xφ ↔ (∃xφ → ∃!xφ))
3	1, 2	sylibr 175	. 2 ⊢ (¬ ∃xφ → ∃*xφ)
4	3	orri 201	1 ⊢ (∃xφ ∨ ∃*xφ)

Syntax hints:  ¬ wn 1   → wi 2   ∨ wo 195  ∃wex 678  ∃!weu 1007  ∃*wmo 1008

This theorem is referenced by:  moexex 1058  mo2icl 1434  mosubop 1911

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-or 197  df-mo 1010

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