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Theorem mooran2 2639
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 2637 . 2 (∃*𝑥(𝜑𝜓) → ∃*𝑥𝜑)
2 olc 864 . . 3 (𝜓 → (𝜑𝜓))
32moimi 2627 . 2 (∃*𝑥(𝜑𝜓) → ∃*𝑥𝜓)
41, 3jca 514 1 (∃*𝑥(𝜑𝜓) → (∃*𝑥𝜑 ∧ ∃*𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  wo 843  ∃*wmo 2620
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-ex 1781  df-mo 2622
This theorem is referenced by:  rmoun  30239
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