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Theorem mooran2 2072
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 2070 . 2 (∃*𝑥(𝜑𝜓) → ∃*𝑥𝜑)
2 olc 700 . . 3 (𝜓 → (𝜑𝜓))
32moimi 2064 . 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 697  ∃*wmo 2000
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003
This theorem is referenced by: (None)
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