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Theorem disjx0 4432
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 3800 . 2  |-  (/)  C_  { (/) }
2 disjxsn 4431 . 2  |- Disj  x  e. 
{ (/) } B
3 disjss1 4413 . 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 3461   (/)c0 3770   {csn 4014  Disj wdisj 4407
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-eu 2272  df-mo 2273  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-rmo 2801  df-v 3097  df-dif 3464  df-in 3468  df-ss 3475  df-nul 3771  df-sn 4015  df-disj 4408
This theorem is referenced by: (None)
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