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Theorem mopick2 2339
 Description: "At most one" can show the existence of a common value. In this case we can infer existence of conjunction from a conjunction of existence, and it is one way to achieve the converse of 19.40 1725. (Contributed by NM, 5-Apr-2004.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
mopick2

Proof of Theorem mopick2
StepHypRef Expression
1 nfmo1 2280 . . . 4
2 nfe1 1894 . . . 4
31, 2nfan 1988 . . 3
4 mopick 2334 . . . . . 6
54ancld 555 . . . . 5
65anim1d 566 . . . 4
7 df-3an 984 . . . 4
86, 7syl6ibr 230 . . 3
93, 8eximd 1937 . 2
1093impia 1202 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370   w3a 982  wex 1657  wmo 2270 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057 This theorem depends on definitions:  df-bi 188  df-an 372  df-3an 984  df-ex 1658  df-nf 1662  df-eu 2273  df-mo 2274 This theorem is referenced by: (None)
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