Theorem abs1

Description: The absolute value of one is one. (Contributed by David A. Wheeler, 16-Jul-2016)

	Ref	Expression
Assertion	abs1	⊢ ( abs ‘ 1 ) = 1

Proof

Step	Hyp	Ref	Expression
1		1re	⊢ 1 ∈ ℝ
2		0le1	⊢ 0 ≤ 1
3		absid	⊢ ( ( 1 ∈ ℝ ∧ 0 ≤ 1 ) → ( abs ‘ 1 ) = 1 )
4	1 2 3	mp2an	⊢ ( abs ‘ 1 ) = 1