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Mirrors > Home > MPE Home > Th. List > adddi | Structured version Visualization version GIF version |
Description: Alias for ax-distr 9882, for naming consistency with adddii 9929. (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 9882 | 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 1031 = wceq 1475 ∈ wcel 1977 (class class class)co 6549 ℂcc 9813 + caddc 9818 · cmul 9820 |
This theorem was proved from axioms: ax-distr 9882 |
This theorem is referenced by: adddir 9910 adddii 9929 adddid 9943 muladd11 10085 mul02lem1 10091 mul02 10093 muladd 10341 nnmulcl 10920 xadddilem 11996 expmul 12767 bernneq 12852 sqoddm1div8 12890 sqreulem 13947 isermulc2 14236 fsummulc2 14358 fsumcube 14630 efexp 14670 efi4p 14706 sinadd 14733 cosadd 14734 cos2tsin 14748 cos01bnd 14755 absefib 14767 efieq1re 14768 demoivreALT 14770 odd2np1 14903 opoe 14925 opeo 14927 gcdmultiple 15107 pythagtriplem12 15369 cncrng 19586 cnlmod 22748 plydivlem4 23855 sinperlem 24036 cxpsqrt 24249 chtub 24737 bcp1ctr 24804 2lgslem3d1 24928 cncvcOLD 26822 hhph 27419 2zrngALT 41738 |
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