Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Subclasses and subsets
sseli
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sselii
Metamath Proof Explorer
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Theorem
sseli
Description:
Membership implication from subclass relationship.
(Contributed by
NM
, 5-Aug-1993)
Ref
Expression
Hypothesis
sseli.1
⊢
A
⊆
B
Assertion
sseli
⊢
C
∈
A
→
C
∈
B
Proof
Step
Hyp
Ref
Expression
1
sseli.1
⊢
A
⊆
B
2
ssel
⊢
A
⊆
B
→
C
∈
A
→
C
∈
B
3
1
2
ax-mp
⊢
C
∈
A
→
C
∈
B