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Theorem readdcli 6838
Description: Closure law for addition of reals. (Contributed by NM, 17-Jan-1997.)
Hypotheses
Ref Expression
recni.1 A
axri.2 B
Assertion
Ref Expression
readdcli (A + B)

Proof of Theorem readdcli
StepHypRef Expression
1 recni.1 . 2 A
2 axri.2 . 2 B
3 readdcl 6805 . 2 ((A B ℝ) → (A + B) ℝ)
41, 2, 3mp2an 402 1 (A + B)
Colors of variables: wff set class
Syntax hints:   wcel 1390  (class class class)co 5455  cr 6710   + caddc 6714
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101  ax-addrcl 6780
This theorem is referenced by:  resubcli  7070  eqneg  7490  2re  7765  3re  7769  4re  7772  5re  7774  6re  7776  7re  7778  8re  7780  9re  7782  10re  7784  numltc  8163
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