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Theorem un0 3575
 Description: The union of a class with the empty set is itself. Theorem 24 of [Suppes] p. 27. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
un0

Proof of Theorem un0
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 noel 3554 . . . 4
21biorfi 396 . . 3
32bicomi 193 . 2
43uneqri 3406 1
 Colors of variables: wff setvar class Syntax hints:   wo 357   wceq 1642   wcel 1710   cun 3207  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-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-nul 3551 This theorem is referenced by:  un00  3586  disjssun  3608  difun2  3629  difdifdir  3637  diftpsn3  3849  sspr  3869  sstp  3870  iununi  4050  prprc2  4122  addcid1  4405  nnsucelrlem3  4426  fvun1  5379  fvunsn  5444  fvsnun1  5447  fvsnun2  5448  sbthlem1  6203
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