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Theorem readdcli 7972
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 7939 . 2 ((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ) → (𝐴 + 𝐵) ∈ ℝ)
41, 2, 3mp2an 426 1 (𝐴 + 𝐵) ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 2148  (class class class)co 5877  cr 7812   + caddc 7816
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-addrcl 7910
This theorem is referenced by:  resubcli  8222  eqneg  8691  2re  8991  3re  8995  4re  8998  5re  9000  6re  9002  7re  9004  8re  9006  9re  9008  numltc  9411  ef01bndlem  11766  ex-fl  14562
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