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Theorem disjx0 4001
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 3461 . 2  |-  (/)  C_  { (/) }
2 disjxsn 4000 . 2  |- Disj  x  e. 
{ (/) } B
3 disjss1 3985 . 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 3129   (/)c0 3422   {csn 3592  Disj wdisj 3979
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rmo 2463  df-v 2739  df-dif 3131  df-in 3135  df-ss 3142  df-nul 3423  df-sn 3598  df-disj 3980
This theorem is referenced by: (None)
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