Theorem moor 2257

Description: "At most one" is still the case when a disjunct is removed. (Contributed by NM, 5-Apr-2004.)

Assertion

Ref	Expression
moor	⊢ (∃*x(φ ∨ ψ) → ∃*xφ)

Proof of Theorem moor

Step	Hyp	Ref	Expression
1		orc 374	. 2 ⊢ (φ → (φ ∨ ψ))
2	1	moimi 2251	1 ⊢ (∃*x(φ ∨ ψ) → ∃*xφ)

Syntax hints:   → wi 4   ∨ wo 357  ∃*wmo 2205

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209

This theorem is referenced by:  mooran2  2259