Metamath Proof Explorer


Theorem rpregt0d

Description: A positive real is real and greater than zero. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypothesis rpred.1 φ A +
Assertion rpregt0d φ A 0 < A

Proof

Step Hyp Ref Expression
1 rpred.1 φ A +
2 1 rpred φ A
3 1 rpgt0d φ 0 < A
4 2 3 jca φ A 0 < A