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Theorem readdcli 7969
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 7936 . 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 5874  cr 7809   + caddc 7813
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-addrcl 7907
This theorem is referenced by:  resubcli  8218  eqneg  8687  2re  8987  3re  8991  4re  8994  5re  8996  6re  8998  7re  9000  8re  9002  9re  9004  numltc  9407  ef01bndlem  11759  ex-fl  14397
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