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Theorem disjx0 4207
Description: An empty collection is disjoint. (Contributed by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
disjx0  |- Disj  x  e.  (/) B

Proof of Theorem disjx0
StepHypRef Expression
1 0ss 3656 . 2  |-  (/)  C_  { (/) }
2 disjxsn 4206 . 2  |- Disj  x  e. 
{ (/) } B
3 disjss1 4188 . 2  |-  ( (/)  C_ 
{ (/) }  ->  (Disj  x  e.  { (/) } B  -> Disj  x  e.  (/) B ) )
41, 2, 3mp2 9 1  |- Disj  x  e.  (/) B
Colors of variables: wff set class
Syntax hints:    C_ wss 3320   (/)c0 3628   {csn 3814  Disj wdisj 4182
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rmo 2713  df-v 2958  df-dif 3323  df-in 3327  df-ss 3334  df-nul 3629  df-sn 3820  df-disj 4183
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