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Theorem readdcli 7747
Description: Closure law for addition of reals. (Contributed by NM, 17-Jan-1997.)
Hypotheses
Ref Expression
recni.1 𝐴 ∈ ℝ
axri.2 𝐵 ∈ ℝ
Assertion
Ref Expression
readdcli (𝐴 + 𝐵) ∈ ℝ

Proof of Theorem readdcli
StepHypRef Expression
1 recni.1 . 2 𝐴 ∈ ℝ
2 axri.2 . 2 𝐵 ∈ ℝ
3 readdcl 7714 . 2 ((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ) → (𝐴 + 𝐵) ∈ ℝ)
41, 2, 3mp2an 422 1 (𝐴 + 𝐵) ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 1465  (class class class)co 5742  cr 7587   + caddc 7591
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-addrcl 7685
This theorem is referenced by:  resubcli  7993  eqneg  8460  2re  8758  3re  8762  4re  8765  5re  8767  6re  8769  7re  8771  8re  8773  9re  8775  numltc  9175  ef01bndlem  11390  ex-fl  12864
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