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Theorem n0f 3793
Description: A nonempty class has at least one element. Proposition 5.17(1) of [TakeutiZaring] p. 20. This version of n0 3794 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 2619 . . . . 5
31, 2cleqf 2646 . . . 4
4 noel 3788 . . . . . 6
54nbn 347 . . . . 5
65albii 1640 . . . 4
73, 6bitr4i 252 . . 3
87necon3abii 2717 . 2
9 df-ex 1613 . 2
108, 9bitr4i 252 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  <->wb 184  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818  F/_wnfc 2605  =/=wne 2652   c0 3784
This theorem is referenced by:  n0  3794  abn0  3804  cp  8330  ordtconlem1  27906
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-nul 3785
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