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Metamath Proof Explorer

Theorem fzo12sn

Description: A 1-based half-open integer interval up to, but not including, 2 is a singleton. (Contributed by Alexander van der Vekens, 31-Jan-2018)

		Ref	Expression
	Assertion	fzo12sn	⊢ ( 1 ..^ 2 ) = { 1 }

Proof

Step	Hyp	Ref	Expression
1		df-2	⊢ 2 = ( 1 + 1 )
2	1	oveq2i	⊢ ( 1 ..^ 2 ) = ( 1 ..^ ( 1 + 1 ) )
3		1z	⊢ 1 ∈ ℤ
4		fzosn	⊢ ( 1 ∈ ℤ → ( 1 ..^ ( 1 + 1 ) ) = { 1 } )
5	3 4	ax-mp	⊢ ( 1 ..^ ( 1 + 1 ) ) = { 1 }
6	2 5	eqtri	⊢ ( 1 ..^ 2 ) = { 1 }