Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Ordinals
orduniss
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ordtri2or
Metamath Proof Explorer
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Unicode
Theorem
orduniss
Description:
An ordinal class includes its union.
(Contributed by
NM
, 13-Sep-2003)
Ref
Expression
Assertion
orduniss
⊢
Ord
⁡
A
→
⋃
A
⊆
A
Proof
Step
Hyp
Ref
Expression
1
ordtr
⊢
Ord
⁡
A
→
Tr
⁡
A
2
df-tr
⊢
Tr
⁡
A
↔
⋃
A
⊆
A
3
1
2
sylib
⊢
Ord
⁡
A
→
⋃
A
⊆
A