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Theorem disjx0 4034
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 3496 . 2  |-  (/)  C_  { (/) }
2 disjxsn 4033 . 2  |- Disj  x  e. 
{ (/) } B
3 disjss1 4015 . 2  |-  ( (/)  C_ 
{ (/) }  ->  (Disj  x  e.  { (/) } B  -> Disj  x  e.  (/) B ) )
41, 2, 3mp2 17 1  |- Disj  x  e.  (/) B
Colors of variables: wff set class
Syntax hints:    C_ wss 3165   (/)c0 3468   {csn 3653  Disj wdisj 4009
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rmo 2564  df-v 2803  df-dif 3168  df-in 3172  df-ss 3179  df-nul 3469  df-sn 3659  df-disj 4010
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