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Theorem euexex 1982
Description: Existential uniqueness and "at most one" double quantification. (Contributed by Jim Kingdon, 28-Dec-2018.)
Hypothesis
Ref Expression
euexex.1  F/
Assertion
Ref Expression
euexex

Proof of Theorem euexex
StepHypRef Expression
1 eu5 1944 . . 3
2 nfmo1 1909 . . . . . 6  F/
3 nfa1 1431 . . . . . . 7  F/
4 nfe1 1382 . . . . . . . 8  F/
54nfmo 1917 . . . . . . 7  F/
63, 5nfim 1461 . . . . . 6  F/
72, 6nfim 1461 . . . . 5  F/
8 euexex.1 . . . . . . 7  F/
98nfmo 1917 . . . . . . 7  F/
10 mopick 1975 . . . . . . . . 9
1110ex 108 . . . . . . . 8
1211com3r 73 . . . . . . 7
138, 9, 12alrimd 1498 . . . . . 6
14 moim 1961 . . . . . . 7
1514spsd 1428 . . . . . 6
1613, 15syl6 29 . . . . 5
177, 16exlimi 1482 . . . 4
1817imp 115 . . 3
191, 18sylbi 114 . 2
2019imp 115 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  wal 1240   F/wnf 1346  wex 1378  weu 1897  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-bndl 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-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901
This theorem is referenced by:  mosubt  2712  funco  4883
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