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Metamath Proof Explorer

Theorem nndivred

Description: A positive integer is one or greater. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses nndivred.1 ⊢ φ → A ∈ ℝ
nndivred.2 ⊢ φ → B ∈ ℕ
Assertion nndivred ⊢ φ → A B ∈ ℝ

Proof

Step Hyp Ref Expression
1 nndivred.1 ⊢ φ → A ∈ ℝ
2 nndivred.2 ⊢ φ → B ∈ ℕ
3 nndivre ⊢ A ∈ ℝ ∧ B ∈ ℕ → A B ∈ ℝ
4 1 2 3 syl2anc ⊢ φ → A B ∈ ℝ