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Theorem mooran2 2259
 Description: "At most one" exports disjunction to conjunction. (Contributed by NM, 5-Apr-2004.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
mooran2 (∃*x(φ ψ) → (∃*xφ ∃*xψ))

Proof of Theorem mooran2
StepHypRef Expression
1 moor 2257 . 2 (∃*x(φ ψ) → ∃*xφ)
2 olc 373 . . 3 (ψ → (φ ψ))
32moimi 2251 . 2 (∃*x(φ ψ) → ∃*xψ)
41, 3jca 518 1 (∃*x(φ ψ) → (∃*xφ ∃*xψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∨ wo 357   ∧ wa 358  ∃*wmo 2205 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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: (None)
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