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Theorem mopick2 1999
 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 1538. (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 hbmo1 1954 . . . 4
2 hbe1 1400 . . . 4
31, 2hban 1455 . . 3
4 mopick 1994 . . . . . 6
54ancld 312 . . . . 5
65anim1d 323 . . . 4
7 df-3an 898 . . . 4
86, 7syl6ibr 155 . . 3
93, 8eximdh 1518 . 2
1093impia 1112 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   w3a 896  wex 1397  wmo 1917 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444 This theorem depends on definitions:  df-bi 114  df-3an 898  df-nf 1366  df-sb 1662  df-eu 1919  df-mo 1920 This theorem is referenced by: (None)
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