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Theorem vn0 3379
 Description: The universal class is not equal to the empty set. (Contributed by NM, 11-Sep-2008.)
Assertion
Ref Expression
vn0 V ≠ ∅

Proof of Theorem vn0
StepHypRef Expression
1 vex 2693 . 2 𝑥 ∈ V
2 ne0i 3375 . 2 (𝑥 ∈ V → V ≠ ∅)
31, 2ax-mp 5 1 V ≠ ∅
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1481   ≠ wne 2309  Vcvv 2690  ∅c0 3369 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 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ne 2310  df-v 2692  df-dif 3079  df-nul 3370 This theorem is referenced by: (None)
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