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Theorem mooran1 2510
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 471 . . 3 ((𝜑𝜓) → 𝜑)
21moimi 2503 . 2 (∃*𝑥𝜑 → ∃*𝑥(𝜑𝜓))
3 moan 2507 . 2 (∃*𝑥𝜓 → ∃*𝑥(𝜑𝜓))
42, 3jaoi 392 1 ((∃*𝑥𝜑 ∨ ∃*𝑥𝜓) → ∃*𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 381  wa 382  ∃*wmo 2454
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-10 2004  ax-12 2031
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-eu 2457  df-mo 2458
This theorem is referenced by: (None)
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