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Theorem zfnuleu 4052
 Description: Show the uniqueness of the empty set (using the Axiom of Extensionality via bm1.1 2124 to strengthen the hypothesis in the form of axnul 4053). (Contributed by NM, 22-Dec-2007.)
Hypothesis
Ref Expression
zfnuleu.1
Assertion
Ref Expression
zfnuleu
Distinct variable group:   ,

Proof of Theorem zfnuleu
StepHypRef Expression
1 zfnuleu.1 . . . 4
2 nbfal 1342 . . . . . 6
32albii 1446 . . . . 5
43exbii 1584 . . . 4
51, 4mpbi 144 . . 3
6 nfv 1508 . . . 4
76bm1.1 2124 . . 3
85, 7ax-mp 5 . 2
93eubii 2008 . 2
108, 9mpbir 145 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 104  wal 1329   wfal 1336  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 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-eu 2002 This theorem is referenced by: (None)
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