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Theorem disjx0 4368
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 3730 . 2  |-  (/)  C_  { (/) }
2 disjxsn 4367 . 2  |- Disj  x  e. 
{ (/) } B
3 disjss1 4350 . 2  |-  ( (/)  C_ 
{ (/) }  ->  (Disj  x  e.  { (/) } B  -> Disj  x  e.  (/)  B ) )
41, 2, 3mp2 9 1  |- Disj  x  e.  (/)  B
Colors of variables: wff setvar class
Syntax hints:    C_ wss 3371   (/)c0 3698   {csn 3935  Disj wdisj 4344
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1672  ax-4 1685  ax-5 1761  ax-6 1808  ax-7 1854  ax-10 1918  ax-11 1923  ax-12 1936  ax-13 2091  ax-ext 2431
This theorem depends on definitions:  df-bi 190  df-or 376  df-an 377  df-tru 1450  df-ex 1667  df-nf 1671  df-sb 1801  df-eu 2303  df-mo 2304  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-rmo 2744  df-v 3014  df-dif 3374  df-in 3378  df-ss 3385  df-nul 3699  df-sn 3936  df-disj 4345
This theorem is referenced by: (None)
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