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Theorem mopick2 2362
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 1679. (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 2295 . . . 4
2 nfe1 1840 . . . 4
31, 2nfan 1928 . . 3
4 mopick 2356 . . . . . 6
54ancld 553 . . . . 5
65anim1d 564 . . . 4
7 df-3an 975 . . . 4
86, 7syl6ibr 227 . . 3
93, 8eximd 1882 . 2
1093impia 1193 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  /\w3a 973  E.wex 1612  E*wmo 2283
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287
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