Metamath Proof Explorer


Theorem absidd

Description: A nonnegative number is its own absolute value. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypotheses resqrcld.1 φA
resqrcld.2 φ0A
Assertion absidd φA=A

Proof

Step Hyp Ref Expression
1 resqrcld.1 φA
2 resqrcld.2 φ0A
3 absid A0AA=A
4 1 2 3 syl2anc φA=A