Metamath Proof Explorer


Theorem leabsd

Description: A real number is less than or equal to its absolute value. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypothesis resqrcld.1
|- ( ph -> A e. RR )
Assertion leabsd
|- ( ph -> A <_ ( abs ` A ) )

Proof

Step Hyp Ref Expression
1 resqrcld.1
 |-  ( ph -> A e. RR )
2 leabs
 |-  ( A e. RR -> A <_ ( abs ` A ) )
3 1 2 syl
 |-  ( ph -> A <_ ( abs ` A ) )