Database
BASIC REAL AND COMPLEX FUNCTIONS
Polynomials
Algebraic numbers
0aa
Next ⟩
1aa
Metamath Proof Explorer
Ascii
Structured
Theorem
0aa
Description:
Zero is algebraic.
(Contributed by
Ender Ting
, 21-Jul-2026)
Ref
Expression
Assertion
0aa
⊢
0 ∈ 𝔸
Proof
Step
Hyp
Ref
Expression
1
qssaa
⊢
ℚ ⊆ 𝔸
2
zssq
⊢
ℤ ⊆ ℚ
3
0z
⊢
0 ∈ ℤ
4
2
3
sselii
⊢
0 ∈ ℚ
5
1
4
sselii
⊢
0 ∈ 𝔸