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Metamath Proof Explorer

Theorem peano2zd

Description: Deduction from second Peano postulate generalized to integers. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypothesis zred.1 ⊢ ( 𝜑 → 𝐴 ∈ ℤ )
Assertion peano2zd ( 𝜑 → ( 𝐴 + 1 ) ∈ ℤ )

Proof

Step Hyp Ref Expression
1 zred.1 ⊢ ( 𝜑 → 𝐴 ∈ ℤ )
2 peano2z ⊢ ( 𝐴 ∈ ℤ → ( 𝐴 + 1 ) ∈ ℤ )
3 1 2 syl ⊢ ( 𝜑 → ( 𝐴 + 1 ) ∈ ℤ )