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Theorem mooran1 2078
 Description: "At most one" imports disjunction to conjunction. (Contributed by NM, 5-Apr-2004.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
mooran1 ((∃*𝑥𝜑 ∨ ∃*𝑥𝜓) → ∃*𝑥(𝜑𝜓))

Proof of Theorem mooran1
StepHypRef Expression
1 simpl 108 . . 3 ((𝜑𝜓) → 𝜑)
21moimi 2071 . 2 (∃*𝑥𝜑 → ∃*𝑥(𝜑𝜓))
3 moan 2075 . 2 (∃*𝑥𝜓 → ∃*𝑥(𝜑𝜓))
42, 3jaoi 706 1 ((∃*𝑥𝜑 ∨ ∃*𝑥𝜓) → ∃*𝑥(𝜑𝜓))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 103   ∨ wo 698  ∃*wmo 2007 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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-eu 2009  df-mo 2010 This theorem is referenced by: (None)
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