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Metamath Proof Explorer

Theorem zringplusg

Description: The addition operation of the ring of integers. (Contributed by Thierry Arnoux, 8-Nov-2017) (Revised by AV, 9-Jun-2019)

Ref Expression
Assertion zringplusg + = ( +g ‘ ℤring )

Proof

Step Hyp Ref Expression
1 zex ⊢ ℤ ∈ V
2 df-zring ⊢ ℤring = ( ℂfld ↾s ℤ )
3 cnfldadd ⊢ + = ( +g ‘ ℂfld )
4 2 3 ressplusg ⊢ ( ℤ ∈ V → + = ( +g ‘ ℤring ) )
5 1 4 ax-mp ⊢ + = ( +g ‘ ℤring )