Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Union
Ordinal arithmetic
2on0
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3on
Metamath Proof Explorer
Ascii
Structured
Theorem
2on0
Description:
Ordinal two is not zero.
(Contributed by
Scott Fenton
, 17-Jun-2011)
Ref
Expression
Assertion
2on0
⊢
2
o
≠ ∅
Proof
Step
Hyp
Ref
Expression
1
df-2o
⊢
2
o
= suc 1
o
2
nsuceq0
⊢
suc 1
o
≠ ∅
3
1
2
eqnetri
⊢
2
o
≠ ∅