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Theorem suc0 4482
Description: The successor of the empty set. (Contributed by NM, 1-Feb-2005.)
Assertion
Ref Expression
suc0  |-  suc  (/)  =  { (/)
}

Proof of Theorem suc0
StepHypRef Expression
1 df-suc 4414 . 2  |-  suc  (/)  =  (
(/)  u.  { (/) } )
2 uncom 3332 . 2  |-  ( (/)  u. 
{ (/) } )  =  ( { (/) }  u.  (/) )
3 un0 3492 . 2  |-  ( {
(/) }  u.  (/) )  =  { (/) }
41, 2, 33eqtri 2320 1  |-  suc  (/)  =  { (/)
}
Colors of variables: wff set class
Syntax hints:    = wceq 1632    u. cun 3163   (/)c0 3468   {csn 3653   suc csuc 4410
This theorem is referenced by:  df1o2  6507  axdc3lem4  8095
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-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-dif 3168  df-un 3170  df-nul 3469  df-suc 4414
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