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Theorem mooran2 2050
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 2048 . 2 (∃*𝑥(𝜑𝜓) → ∃*𝑥𝜑)
2 olc 685 . . 3 (𝜓 → (𝜑𝜓))
32moimi 2042 . 2 (∃*𝑥(𝜑𝜓) → ∃*𝑥𝜓)
41, 3jca 304 1 (∃*𝑥(𝜑𝜓) → (∃*𝑥𝜑 ∧ ∃*𝑥𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wo 682  ∃*wmo 1978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-eu 1980  df-mo 1981
This theorem is referenced by: (None)
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