Metamath Proof Explorer

Theorem absrpcld

Description: The absolute value of a nonzero number is a positive real. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypotheses abscld.1 φ A
absne0d.2 φ A 0
Assertion absrpcld φ A +


Step Hyp Ref Expression
1 abscld.1 φ A
2 absne0d.2 φ A 0
3 absrpcl A A 0 A +
4 1 2 3 syl2anc φ A +