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Metamath Proof Explorer

Theorem oddz

Description: An odd number is an integer. (Contributed by AV, 14-Jun-2020)

Ref Expression
Assertion oddz ( 𝑍 ∈ Odd → 𝑍 ∈ ℤ )

Proof

Step Hyp Ref Expression
1 isodd ⊢ ( 𝑍 ∈ Odd ↔ ( 𝑍 ∈ ℤ ∧ ( ( 𝑍 + 1 ) / 2 ) ∈ ℤ ) )
2 1 simplbi ⊢ ( 𝑍 ∈ Odd → 𝑍 ∈ ℤ )