ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  addcli GIF version

Theorem addcli 7777
Description: Closure law for addition. (Contributed by NM, 23-Nov-1994.)
Hypotheses
Ref Expression
axi.1 𝐴 ∈ ℂ
axi.2 𝐵 ∈ ℂ
Assertion
Ref Expression
addcli (𝐴 + 𝐵) ∈ ℂ

Proof of Theorem addcli
StepHypRef Expression
1 axi.1 . 2 𝐴 ∈ ℂ
2 axi.2 . 2 𝐵 ∈ ℂ
3 addcl 7752 . 2 ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 + 𝐵) ∈ ℂ)
41, 2, 3mp2an 422 1 (𝐴 + 𝐵) ∈ ℂ
Colors of variables: wff set class
Syntax hints:  wcel 1480  (class class class)co 5774  cc 7625   + caddc 7630
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-addcl 7723
This theorem is referenced by:  negdii  8053  eqneg  8499  nummac  9233  binom2i  10408  3dvds2dec  11569
  Copyright terms: Public domain W3C validator