Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Ordinals
onn0
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suceq
Metamath Proof Explorer
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Theorem
onn0
Description:
The class of all ordinal numbers is not empty.
(Contributed by
NM
, 17-Sep-1995)
Ref
Expression
Assertion
onn0
⊢
On
≠
∅
Proof
Step
Hyp
Ref
Expression
1
0elon
⊢
∅
∈
On
2
1
ne0ii
⊢
On
≠
∅