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Theorem mooran1 2702
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 470 . . 3 ((𝜑𝜓) → 𝜑)
21moimi 2694 . 2 (∃*𝑥𝜑 → ∃*𝑥(𝜑𝜓))
3 moan 2699 . 2 (∃*𝑥𝜓 → ∃*𝑥(𝜑𝜓))
42, 3jaoi 875 1 ((∃*𝑥𝜑 ∨ ∃*𝑥𝜓) → ∃*𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  wo 865  ∃*wmo 2633
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-ex 1860  df-mo 2635
This theorem is referenced by: (None)
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