Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
The universal class
issetri
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eqvisset
Metamath Proof Explorer
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Theorem
issetri
Description:
A way to say "
A
is a set" (inference form).
(Contributed by
NM
, 21-Jun-1993)
Ref
Expression
Hypothesis
issetri.1
⊢
∃
x
x
=
A
Assertion
issetri
⊢
A
∈
V
Proof
Step
Hyp
Ref
Expression
1
issetri.1
⊢
∃
x
x
=
A
2
isset
⊢
A
∈
V
↔
∃
x
x
=
A
3
1
2
mpbir
⊢
A
∈
V