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Theorem neq0 3560
 Description: A nonempty class has at least one element. Proposition 5.17(1) of [TakeutiZaring] p. 20. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
neq0
Distinct variable group:   ,

Proof of Theorem neq0
StepHypRef Expression
1 df-ne 2518 . 2
2 n0 3559 . 2
31, 2bitr3i 242 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 176  wex 1541   wceq 1642   wcel 1710   wne 2516  c0 3550 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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:  eq0  3564  ralidm  3653  snprc  3788  pwpw0  3855  sssn  3864  pwsnALT  3882  uni0b  3916  nndisjeq  4429  isomin  5496  erdisj  5972
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