Metamath Proof Explorer


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