Theorem addass 8315

Description: Alias for ax-addass 8287, for naming consistency with addassi 8340. (Contributed by NM, 10-Mar-2008.)

Assertion

Ref	Expression
addass	⊢ ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ∧ 𝐶 ∈ ℂ) → ((𝐴 + 𝐵) + 𝐶) = (𝐴 + (𝐵 + 𝐶)))

Proof of Theorem addass

Step	Hyp	Ref	Expression
1		ax-addass 8287	1 ⊢ ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ∧ 𝐶 ∈ ℂ) → ((𝐴 + 𝐵) + 𝐶) = (𝐴 + (𝐵 + 𝐶)))

This proof depends on syntax axioms:   → wi 4   ∧ w3a 1009   = wceq 1402   ∈ wcel 2209  (class class class)co 6088  ℂcc 8183   + caddc 8188

This proof depends on axioms:  ax-addass 8287

This theorem is used by:  addassi  8340  addassd  8354  add12  8491  add32  8492  add32r  8493  add4  8494  nnaddcl  9333  uzaddcl  10001  xaddass  10287  fztp  10501  ser3add  10979  expadd  11038  bernneq  11118  faclbnd6  11203  resqrexlemover  11797  clim2ser  12127  clim2ser2  12128  summodclem3  12171  isumsplit  12282  cvgratnnlemseq  12317  odd2np1lem  12663  prmlem0  13248  cncrng  15014  ptolemy  16068  bcp1ctr  16323