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Theorem adddi 7011
Description: Alias for ax-distr 6986, for naming consistency with adddii 7035. (Contributed by NM, 10-Mar-2008.)
Assertion
Ref Expression
adddi ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ∧ 𝐶 ∈ ℂ) → (𝐴 · (𝐵 + 𝐶)) = ((𝐴 · 𝐵) + (𝐴 · 𝐶)))

Proof of Theorem adddi
StepHypRef Expression
1 ax-distr 6986 1 ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ∧ 𝐶 ∈ ℂ) → (𝐴 · (𝐵 + 𝐶)) = ((𝐴 · 𝐵) + (𝐴 · 𝐶)))
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 885   = wceq 1243  wcel 1393  (class class class)co 5512  cc 6885   + caddc 6890   · cmul 6892
This theorem was proved from axioms:  ax-distr 6986
This theorem is referenced by:  adddir  7016  adddii  7035  adddid  7049  muladd11  7144  cnegex  7187  muladd  7379  nnmulcl  7933  expmul  9274  bernneq  9343  iisermulc2  9834
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