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Theorem disjx0 4435
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 3807 . 2  |-  (/)  C_  { (/) }
2 disjxsn 4434 . 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 3469   (/)c0 3778   {csn 4020  Disj wdisj 4410
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-eu 2272  df-mo 2273  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-rmo 2815  df-v 3108  df-dif 3472  df-in 3476  df-ss 3483  df-nul 3779  df-sn 4021  df-disj 4411
This theorem is referenced by: (None)
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