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Theorem mooran2 2516
 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(𝜑𝜓) → (∃*𝑥𝜑 ∧ ∃*𝑥𝜓))

Proof of Theorem mooran2
StepHypRef Expression
1 moor 2514 . 2 (∃*𝑥(𝜑𝜓) → ∃*𝑥𝜑)
2 olc 398 . . 3 (𝜓 → (𝜑𝜓))
32moimi 2508 . 2 (∃*𝑥(𝜑𝜓) → ∃*𝑥𝜓)
41, 3jca 553 1 (∃*𝑥(𝜑𝜓) → (∃*𝑥𝜑 ∧ ∃*𝑥𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∨ wo 382   ∧ wa 383  ∃*wmo 2459 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-eu 2462  df-mo 2463 This theorem is referenced by: (None)
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