Metamath Proof Explorer


Theorem rprecred

Description: Closure law for reciprocation of positive reals. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypothesis rpred.1 φ A +
Assertion rprecred φ 1 A

Proof

Step Hyp Ref Expression
1 rpred.1 φ A +
2 1 rpreccld φ 1 A +
3 2 rpred φ 1 A