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Theorem n0f 3558
Description: A nonempty class has at least one element. Proposition 5.17(1) of [TakeutiZaring] p. 20. This version of n0 3559 requires only that not be free in, rather than not occur in, . (Contributed by NM, 17-Oct-2003.)
Hypothesis
Ref Expression
n0f.1  F/_
Assertion
Ref Expression
n0f

Proof of Theorem n0f
StepHypRef Expression
1 n0f.1 . . . . 5  F/_
2 nfcv 2489 . . . . 5  F/_
31, 2cleqf 2513 . . . 4
4 noel 3554 . . . . . 6
54nbn 336 . . . . 5
65albii 1566 . . . 4
73, 6bitr4i 243 . . 3
87necon3abii 2546 . 2
9 df-ex 1542 . 2
108, 9bitr4i 243 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wb 176  wal 1540  wex 1541   wceq 1642   wcel 1710   F/_wnfc 2476   wne 2516  c0 3550
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-nul 3551
This theorem is referenced by:  n0  3559  abn0  3568
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