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Metamath Proof Explorer

Theorem nn0sub2

Description: Subtraction of nonnegative integers. (Contributed by NM, 4-Sep-2005)

Ref Expression
Assertion nn0sub2 ⊢ M ∈ ℕ 0 ∧ N ∈ ℕ 0 ∧ M ≤ N → N − M ∈ ℕ 0

Proof

Step Hyp Ref Expression
1 nn0sub ⊢ M ∈ ℕ 0 ∧ N ∈ ℕ 0 → M ≤ N ↔ N − M ∈ ℕ 0
2 1 biimp3a ⊢ M ∈ ℕ 0 ∧ N ∈ ℕ 0 ∧ M ≤ N → N − M ∈ ℕ 0