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Theorem disjx0 3813
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 3306 . 2  |-  (/)  C_  { (/) }
2 disjxsn 3812 . 2  |- Disj  x  e. 
{ (/) } B
3 disjss1 3801 . 2  |-  ( (/)  C_ 
{ (/) }  ->  (Disj  x  e.  { (/) } B  -> Disj  x  e.  (/)  B ) )
41, 2, 3mp2 16 1  |- Disj  x  e.  (/)  B
Colors of variables: wff set class
Syntax hints:    C_ wss 2986   (/)c0 3272   {csn 3425  Disj wdisj 3795
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-eu 1948  df-mo 1949  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rmo 2363  df-v 2616  df-dif 2988  df-in 2992  df-ss 2999  df-nul 3273  df-sn 3431  df-disj 3796
This theorem is referenced by: (None)
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