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Theorem complV 4070
 Description: The complement of the universe is the empty set. (Contributed by SF, 2-Jan-2018.)
Assertion
Ref Expression
complV

Proof of Theorem complV
StepHypRef Expression
1 compldif 4069 . 2
2 df-nul 3551 . 2
31, 2eqtr4i 2376 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1642  cvv 2859   ∼ ccompl 3205   cdif 3206  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:  compl0  4071  incompl  4073  0ex  4110  nulnnn  4556
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