Metamath Proof Explorer


Theorem z4even

Description: 2 divides 4. That means 4 is even. (Contributed by AV, 23-Jul-2020) (Revised by AV, 4-Jul-2021)

Ref Expression
Assertion z4even ⊢ 2 ∥ 4

Proof

Step Hyp Ref Expression
1 2z ⊢ 2 ∈ ℤ
2 dvdsmul1 ⊢ 2 ∈ ℤ ∧ 2 ∈ ℤ → 2 ∥ 2 ⋅ 2
3 1 1 2 mp2an ⊢ 2 ∥ 2 ⋅ 2
4 2t2e4 ⊢ 2 ⋅ 2 = 4
5 3 4 breqtri ⊢ 2 ∥ 4