Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Union
Ordinal arithmetic
1on
Next ⟩
2on
Metamath Proof Explorer
Ascii
Structured
Theorem
1on
Description:
Ordinal 1 is an ordinal number.
(Contributed by
NM
, 29-Oct-1995)
Ref
Expression
Assertion
1on
⊢
1
o
∈ On
Proof
Step
Hyp
Ref
Expression
1
df-1o
⊢
1
o
= suc ∅
2
0elon
⊢
∅ ∈ On
3
2
onsuci
⊢
suc ∅ ∈ On
4
1
3
eqeltri
⊢
1
o
∈ On