Metamath Proof Explorer


Theorem rprene0d

Description: A positive real is a nonzero real number. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypothesis rpred.1 φ A +
Assertion rprene0d φ A A 0

Proof

Step Hyp Ref Expression
1 rpred.1 φ A +
2 1 rpred φ A
3 1 rpne0d φ A 0
4 2 3 jca φ A A 0