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Theorem eunex 4476
 Description: Existential uniqueness implies there is a value for which the wff argument is false. (Contributed by Jim Kingdon, 29-Dec-2018.)
Assertion
Ref Expression
eunex

Proof of Theorem eunex
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1508 . . 3
21eu3 2045 . 2
3 dtruex 4474 . . . . 5
4 nfa1 1521 . . . . . 6
5 sp 1488 . . . . . . 7
65con3d 620 . . . . . 6
74, 6eximd 1591 . . . . 5
83, 7mpi 15 . . . 4
98exlimiv 1577 . . 3
109adantl 275 . 2
112, 10sylbi 120 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103  wal 1329   wceq 1331  wex 1468  weu 1999 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-setind 4452 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2002  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ne 2309  df-ral 2421  df-v 2688  df-dif 3073  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533 This theorem is referenced by: (None)
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