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Theorem n0f 3628
 Description: A nonempty class has at least one element. Proposition 5.17(1) of [TakeutiZaring] p. 20. This version of n0 3629 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 2571 . . . . 5
31, 2cleqf 2595 . . . 4
4 noel 3624 . . . . . 6
54nbn 337 . . . . 5
65albii 1575 . . . 4
73, 6bitr4i 244 . . 3
87necon3abii 2628 . 2
9 df-ex 1551 . 2
108, 9bitr4i 244 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 177  wal 1549  wex 1550   wceq 1652   wcel 1725  wnfc 2558   wne 2598  c0 3620 This theorem is referenced by:  n0  3629  abn0  3638  cp  7807 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-v 2950  df-dif 3315  df-nul 3621
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