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Theorem eunex 4239
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 1418 . . 3  F/
21eu3 1943 . 2
3 dtruex 4237 . . . . 5
4 nfa1 1431 . . . . . 6  F/
5 sp 1398 . . . . . . 7
65con3d 560 . . . . . 6
74, 6eximd 1500 . . . . 5
83, 7mpi 15 . . . 4
98exlimiv 1486 . . 3
109adantl 262 . 2
112, 10sylbi 114 1
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 97  wal 1240   wceq 1242  wex 1378  weu 1897
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-in1 544  ax-in2 545  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-bnd 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-setind 4220
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ne 2203  df-ral 2305  df-v 2553  df-dif 2914  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373
This theorem is referenced by: (None)
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