Theorem adddi 7105

Description: Alias for ax-distr 7080, for naming consistency with adddii 7129. (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

Step	Hyp	Ref	Expression
1		ax-distr 7080	1 ⊢ ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ∧ 𝐶 ∈ ℂ) → (𝐴 · (𝐵 + 𝐶)) = ((𝐴 · 𝐵) + (𝐴 · 𝐶)))

Syntax hints:   → wi 4   ∧ w3a 919   = wceq 1284   ∈ wcel 1433  (class class class)co 5532  ℂcc 6979   + caddc 6984   · cmul 6986

This theorem was proved from axioms:  ax-distr 7080

This theorem is referenced by:  adddir  7110  adddii  7129  adddid  7143  muladd11  7241  cnegex  7286  muladd  7488  nnmulcl  8060  expmul  9521  bernneq  9593  sqoddm1div8  9625  iisermulc2  10178  odd2np1  10272  opoe  10295  opeo  10297  gcdmultiple  10409