Theorem fzo0ss1

Description: Subset relationship for half-open integer ranges with lower bounds 0 and 1. (Contributed by Alexander van der Vekens, 18-Mar-2018)

	Ref	Expression
Assertion	fzo0ss1	⊢ ( 1 ..^ 𝑁 ) ⊆ ( 0 ..^ 𝑁 )

Proof

Step	Hyp	Ref	Expression
1		1eluzge0	⊢ 1 ∈ ( ℤ≥ ‘ 0 )
2		fzoss1	⊢ ( 1 ∈ ( ℤ≥ ‘ 0 ) → ( 1 ..^ 𝑁 ) ⊆ ( 0 ..^ 𝑁 ) )
3	1 2	ax-mp	⊢ ( 1 ..^ 𝑁 ) ⊆ ( 0 ..^ 𝑁 )