Theorem suc0 3043

Description: The successor of the empty set.

Assertion

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

Proof of Theorem suc0

Step	Hyp	Ref	Expression
1		df-suc 2954	. 2 |- suc (/) = ((/) u. {(/)})
2		uncom 2176	. 2 |- ((/) u. {(/)}) = ({(/)} u. (/))
3		un0 2297	. 2 |- ({(/)} u. (/)) = {(/)}
4	1, 2, 3	3eqtr 1499	1 |- suc (/) = {(/)}

Syntax hints:   = wceq 956   u. cun 2045  (/)c0 2280  {csn 2409  suc csuc 2950

This theorem is referenced by:  df1o2 4140

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-dif 2049  df-un 2050  df-nul 2281  df-suc 2954

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