Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Union
Ordinal arithmetic
4on
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Metamath Proof Explorer
Ascii
Structured
Theorem
4on
Description:
Ordinal 4 is an ordinal number.
(Contributed by
Mario Carneiro
, 5-Jan-2016)
Ref
Expression
Assertion
4on
⊢
4
o
∈ On
Proof
Step
Hyp
Ref
Expression
1
df-4o
⊢
4
o
= suc 3
o
2
3on
⊢
3
o
∈ On
3
2
onsuci
⊢
suc 3
o
∈ On
4
1
3
eqeltri
⊢
4
o
∈ On