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 ) |
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 ) |