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Theorem mooran1 1969
 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(φ ψ))

Proof of Theorem mooran1
StepHypRef Expression
1 simpl 102 . . 3 ((φ ψ) → φ)
21moimi 1962 . 2 (∃*xφ∃*x(φ ψ))
3 moan 1966 . 2 (∃*xψ∃*x(φ ψ))
42, 3jaoi 635 1 ((∃*xφ ∃*xψ) → ∃*x(φ ψ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ∨ wo 628  ∃*wmo 1898 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901 This theorem is referenced by: (None)
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