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Theorem mooran1 2098
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 109 . . 3 ((𝜑𝜓) → 𝜑)
21moimi 2091 . 2 (∃*𝑥𝜑 → ∃*𝑥(𝜑𝜓))
3 moan 2095 . 2 (∃*𝑥𝜓 → ∃*𝑥(𝜑𝜓))
42, 3jaoi 716 1 ((∃*𝑥𝜑 ∨ ∃*𝑥𝜓) → ∃*𝑥(𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  wo 708  ∃*wmo 2027
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030
This theorem is referenced by: (None)
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