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Theorem compl0 4071
 Description: The complement of the empty set is the universe. (Contributed by SF, 2-Jan-2018.)
Assertion
Ref Expression
compl0 = V

Proof of Theorem compl0
StepHypRef Expression
1 complV 4070 . . 3 ∼ V =
21compleqi 3244 . 2 ∼ ∼ V = ∼
3 dblcompl 3227 . 2 ∼ ∼ V = V
42, 3eqtr3i 2375 1 = V
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642  Vcvv 2859   ∼ ccompl 3205  ∅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-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-ss 3259  df-nul 3551 This theorem is referenced by: (None)
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