Theorem suc0 3049

Description: The successor of the empty set.

Assertion

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

Proof of Theorem suc0

Step	Hyp	Ref	Expression
1		df-suc 2960	. 2 |- suc (/) = ((/) u. {(/)})
2		uncom 2179	. 2 |- ((/) u. {(/)}) = ({(/)} u. (/))
3		un0 2301	. 2 |- ({(/)} u. (/)) = {(/)}
4	1, 2, 3	3eqtr 1502	1 |- suc (/) = {(/)}

Syntax hints:   = wceq 958   u. cun 2048  (/)c0 2283  {csn 2413  suc csuc 2956

This theorem is referenced by:  df1o2 4146

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-v 1815  df-dif 2052  df-un 2053  df-nul 2284  df-suc 2960

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