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Metamath Proof Explorer

Theorem fzonnsub2

Description: If M < N then N - M is a positive integer. (Contributed by Mario Carneiro, 1-Jan-2017)

Ref Expression
Assertion fzonnsub2 ⊢ K ∈ M ..^ N → N − M ∈ ℕ

Proof

Step Hyp Ref Expression
1 elfzolt3b ⊢ K ∈ M ..^ N → M ∈ M ..^ N
2 fzonnsub ⊢ M ∈ M ..^ N → N − M ∈ ℕ
3 1 2 syl ⊢ K ∈ M ..^ N → N − M ∈ ℕ