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ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Replacement
Theorems requiring empty set existence
intv
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Metamath Proof Explorer
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Theorem
intv
Description:
The intersection of the universal class is empty.
(Contributed by
NM
, 11-Sep-2008)
Ref
Expression
Assertion
intv
⊢
⋂
V
=
∅
Proof
Step
Hyp
Ref
Expression
1
0ex
⊢
∅
∈
V
2
int0el
⊢
∅
∈
V
→
⋂
V
=
∅
3
1
2
ax-mp
⊢
⋂
V
=
∅