Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
The difference, union, and intersection of two classes
The union of two classes
ssun2
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ssun3
Metamath Proof Explorer
Ascii
Structured
Theorem
ssun2
Description:
Subclass relationship for union of classes.
(Contributed by
NM
, 30-Aug-1993)
Ref
Expression
Assertion
ssun2
⊢
𝐴
⊆ (
𝐵
∪
𝐴
)
Proof
Step
Hyp
Ref
Expression
1
ssun1
⊢
𝐴
⊆ (
𝐴
∪
𝐵
)
2
uncom
⊢
(
𝐴
∪
𝐵
) = (
𝐵
∪
𝐴
)
3
1
2
sseqtri
⊢
𝐴
⊆ (
𝐵
∪
𝐴
)