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Theorem mopick2 2350
 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 1620. (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 2294 . . . 4
2 nfe1 1748 . . . 4
31, 2nfan 1847 . . 3
4 mopick 2345 . . . . . 6
54ancld 538 . . . . 5
65anim1d 549 . . . 4
7 df-3an 939 . . . 4
86, 7syl6ibr 220 . . 3
93, 8eximd 1787 . 2
1093impia 1151 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   w3a 937  wex 1551  wmo 2284 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288
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