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Theorem mooran2 2666
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 2664 . 2 (∃*𝑥(𝜑𝜓) → ∃*𝑥𝜑)
2 olc 398 . . 3 (𝜓 → (𝜑𝜓))
32moimi 2658 . 2 (∃*𝑥(𝜑𝜓) → ∃*𝑥𝜓)
41, 3jca 555 1 (∃*𝑥(𝜑𝜓) → (∃*𝑥𝜑 ∧ ∃*𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 382  wa 383  ∃*wmo 2608
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-10 2168  ax-12 2196
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1854  df-nf 1859  df-eu 2611  df-mo 2612
This theorem is referenced by: (None)
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