Theorem suc0 3047

Description: The successor of the empty set.

Assertion

Ref	Expression
suc0	|- suc (/) = {(/)}

Proof of Theorem suc0

Step	Hyp	Ref	Expression
1		df-suc 2981	. 2 |- suc (/) = ((/) u. {(/)})
2		uncom 2228	. 2 |- ((/) u. {(/)}) = ({(/)} u. (/))
3		un0 2350	. 2 |- ({(/)} u. (/)) = {(/)}
4	1, 2, 3	3eqtri 1542	1 |- suc (/) = {(/)}

Syntax hints:   = wceq 992   u. cun 2097  (/)c0 2332  {csn 2467  suc csuc 2977

This theorem is referenced by:  df1o2 4276

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 998  ax-gen 999  ax-8 1000  ax-10 1002  ax-12 1004  ax-17 1007  ax-4 1009  ax-5o 1011  ax-6o 1014  ax-9o 1159  ax-10o 1177  ax-16 1247  ax-11o 1255  ax-ext 1500

This theorem depends on definitions:  df-bi 145  df-or 222  df-an 223  df-ex 1017  df-sb 1209  df-clab 1506  df-cleq 1511  df-clel 1514  df-v 1858  df-dif 2101  df-un 2102  df-nul 2333  df-suc 2981

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