Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Union
Ordinals (continued)
sucex
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Metamath Proof Explorer
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Theorem
sucex
Description:
The successor of a set is a set.
(Contributed by
NM
, 30-Aug-1993)
Ref
Expression
Hypothesis
sucex.1
⊢
A
∈
V
Assertion
sucex
⊢
suc
⁡
A
∈
V
Proof
Step
Hyp
Ref
Expression
1
sucex.1
⊢
A
∈
V
2
sucexg
⊢
A
∈
V
→
suc
⁡
A
∈
V
3
1
2
ax-mp
⊢
suc
⁡
A
∈
V