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Theorem euabex 4158
 Description: The abstraction of a wff with existential uniqueness exists. (Contributed by NM, 25-Nov-1994.)
Assertion
Ref Expression
euabex

Proof of Theorem euabex
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 euabsn2 3602 . 2
2 vex 2694 . . . . 5
32snex 4119 . . . 4
4 eleq1 2204 . . . 4
53, 4mpbiri 167 . . 3
65exlimiv 1574 . 2
71, 6sylbi 120 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1332  wex 1469  weu 1990   wcel 2112  cab 2127  cvv 2691  csn 3534 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-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-14 2115  ax-ext 2123  ax-sep 4056  ax-pow 4108 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1732  df-eu 1993  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-v 2693  df-in 3084  df-ss 3091  df-pw 3519  df-sn 3540 This theorem is referenced by: (None)
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