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Metamath Proof Explorer

Theorem oddp1div2z

Description: The result of dividing an odd number increased by 1 and then divided by 2 is an integer. (Contributed by AV, 15-Jun-2020)

Ref Expression
Assertion oddp1div2z ⊢ Z ∈ Odd → Z + 1 2 ∈ ℤ

Proof

Step Hyp Ref Expression
1 isodd ⊢ Z ∈ Odd ↔ Z ∈ ℤ ∧ Z + 1 2 ∈ ℤ
2 1 simprbi ⊢ Z ∈ Odd → Z + 1 2 ∈ ℤ