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Theorem readdcli 7246
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 7213 . 2 ((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ) → (𝐴 + 𝐵) ∈ ℝ)
41, 2, 3mp2an 417 1 (𝐴 + 𝐵) ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 1434  (class class class)co 5563  cr 7094   + caddc 7098
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106  ax-addrcl 7187
This theorem is referenced by:  resubcli  7490  eqneg  7939  2re  8228  3re  8232  4re  8235  5re  8237  6re  8239  7re  8241  8re  8243  9re  8245  numltc  8635  ex-fl  10823
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