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Metamath Proof Explorer

Theorem resubcld

Description: Closure law for subtraction of reals. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses renegcld.1 ⊢ φ → A ∈ ℝ
resubcld.2 ⊢ φ → B ∈ ℝ
Assertion resubcld ⊢ φ → A − B ∈ ℝ

Proof

Step Hyp Ref Expression
1 renegcld.1 ⊢ φ → A ∈ ℝ
2 resubcld.2 ⊢ φ → B ∈ ℝ
3 resubcl ⊢ A ∈ ℝ ∧ B ∈ ℝ → A − B ∈ ℝ
4 1 2 3 syl2anc ⊢ φ → A − B ∈ ℝ