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Theorem n0f 3370
 Description: A nonempty class has at least one element. Proposition 5.17(1) of [TakeutiZaring] p. 20. This version of n0 3371 requires only that not be free in, rather than not occur in, . (Contributed by NM, 17-Oct-2003.)
Hypothesis
Ref Expression
n0f.1
Assertion
Ref Expression
n0f

Proof of Theorem n0f
StepHypRef Expression
1 n0f.1 . . . . 5
2 nfcv 2385 . . . . 5
31, 2cleqf 2409 . . . 4
4 noel 3366 . . . . . 6
54nbn 338 . . . . 5
65albii 1554 . . . 4
73, 6bitr4i 245 . . 3
87necon3abii 2442 . 2
9 df-ex 1538 . 2
108, 9bitr4i 245 1
 Colors of variables: wff set class Syntax hints:   wn 5   wb 178  wal 1532  wex 1537   wceq 1619   wcel 1621  wnfc 2372   wne 2412  c0 3362 This theorem is referenced by:  n0  3371  abn0  3380  cp  7445 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-v 2729  df-dif 3081  df-nul 3363
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