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Mirrors > Home > MPE Home > Th. List > adddi | Structured version Visualization version GIF version |
Description: Alias for ax-distr 11220, for naming consistency with adddii 11271. (Contributed by NM, 10-Mar-2008.) |
Ref | Expression |
---|---|
adddi | ⊢ ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ∧ 𝐶 ∈ ℂ) → (𝐴 · (𝐵 + 𝐶)) = ((𝐴 · 𝐵) + (𝐴 · 𝐶))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-distr 11220 | 1 ⊢ ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ∧ 𝐶 ∈ ℂ) → (𝐴 · (𝐵 + 𝐶)) = ((𝐴 · 𝐵) + (𝐴 · 𝐶))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1086 = wceq 1537 ∈ wcel 2106 (class class class)co 7431 ℂcc 11151 + caddc 11156 · cmul 11158 |
This theorem was proved from axioms: ax-distr 11220 |
This theorem is referenced by: adddir 11250 adddii 11271 adddid 11283 muladd11 11429 mul02lem1 11435 mul02 11437 muladd 11693 nnmulcl 12288 xadddilem 13333 expmul 14145 bernneq 14265 sqoddm1div8 14279 sqreulem 15395 isermulc2 15691 fsummulc2 15817 fsumcube 16093 efexp 16134 efi4p 16170 sinadd 16197 cosadd 16198 cos2tsin 16212 cos01bnd 16219 absefib 16231 efieq1re 16232 demoivreALT 16234 odd2np1 16375 opoe 16397 opeo 16399 pythagtriplem12 16860 cncrng 21419 cncrngOLD 21420 cnlmod 25187 plydivlem4 26353 sinperlem 26537 cxpsqrt 26760 chtub 27271 bcp1ctr 27338 2lgslem3d1 27462 cncvcOLD 30612 hhph 31207 2zrngALT 48098 |
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