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Metamath Proof Explorer

Theorem uzssd3

Description: Subset relationship for two sets of upper integers. (Contributed by Glauco Siliprandi, 23-Oct-2021)

Ref Expression
Hypothesis uzssd3.1 ⊢ 𝑍 = ( ℤ≥ ‘ 𝑀 )
Assertion uzssd3 ( 𝑁 ∈ 𝑍 → ( ℤ≥ ‘ 𝑁 ) ⊆ 𝑍 )

Proof

Step Hyp Ref Expression
1 uzssd3.1 ⊢ 𝑍 = ( ℤ≥ ‘ 𝑀 )
2 id ⊢ ( 𝑁 ∈ 𝑍 → 𝑁 ∈ 𝑍 )
3 1 2 uzssd2 ⊢ ( 𝑁 ∈ 𝑍 → ( ℤ≥ ‘ 𝑁 ) ⊆ 𝑍 )