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Metamath Proof Explorer

Theorem rpdivcld

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

Ref Expression
Hypotheses rpred.1 ⊢ φ → A ∈ ℝ +
rpaddcld.1 ⊢ φ → B ∈ ℝ +
Assertion rpdivcld ⊢ φ → A B ∈ ℝ +

Proof

Step Hyp Ref Expression
1 rpred.1 ⊢ φ → A ∈ ℝ +
2 rpaddcld.1 ⊢ φ → B ∈ ℝ +
3 rpdivcl ⊢ A ∈ ℝ + ∧ B ∈ ℝ + → A B ∈ ℝ +
4 1 2 3 syl2anc ⊢ φ → A B ∈ ℝ +