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Theorem disjx0 4434
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 3813 . 2  |-  (/)  C_  { (/) }
2 disjxsn 4433 . 2  |- Disj  x  e. 
{ (/) } B
3 disjss1 4416 . 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 3783   {csn 4016  Disj wdisj 4410
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-eu 2288  df-mo 2289  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-rmo 2812  df-v 3108  df-dif 3464  df-in 3468  df-ss 3475  df-nul 3784  df-sn 4017  df-disj 4411
This theorem is referenced by: (None)
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