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Metamath Proof Explorer

Theorem iccssred

Description: A closed real interval is a set of reals. (Contributed by Glauco Siliprandi, 11-Dec-2019)

Ref Expression
Hypotheses iccssred.1 ⊢ φ → A ∈ ℝ
iccssred.2 ⊢ φ → B ∈ ℝ
Assertion iccssred ⊢ φ → A B ⊆ ℝ

Proof

Step Hyp Ref Expression
1 iccssred.1 ⊢ φ → A ∈ ℝ
2 iccssred.2 ⊢ φ → B ∈ ℝ
3 iccssre ⊢ A ∈ ℝ ∧ B ∈ ℝ → A B ⊆ ℝ
4 1 2 3 syl2anc ⊢ φ → A B ⊆ ℝ