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Mirrors > Home > MPE Home > Th. List > addass | Structured version Visualization version GIF version |
Description: Alias for ax-addass 11177, for naming consistency with addassi 11228. (Contributed by NM, 10-Mar-2008.) |
Ref | Expression |
---|---|
addass | ⊢ ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ∧ 𝐶 ∈ ℂ) → ((𝐴 + 𝐵) + 𝐶) = (𝐴 + (𝐵 + 𝐶))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-addass 11177 | 1 ⊢ ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ∧ 𝐶 ∈ ℂ) → ((𝐴 + 𝐵) + 𝐶) = (𝐴 + (𝐵 + 𝐶))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1085 = wceq 1539 ∈ wcel 2104 (class class class)co 7411 ℂcc 11110 + caddc 11115 |
This theorem was proved from axioms: ax-addass 11177 |
This theorem is referenced by: addassi 11228 addassd 11240 00id 11393 addlid 11401 add12 11435 add32 11436 add32r 11437 add4 11438 nnaddcl 12239 uzaddcl 12892 xaddass 13232 fztp 13561 seradd 14014 expadd 14074 bernneq 14196 faclbnd6 14263 hashgadd 14341 swrds2 14895 clim2ser 15605 clim2ser2 15606 summolem3 15664 isumsplit 15790 fsumcube 16008 odd2np1lem 16287 prmlem0 17043 cnaddablx 19777 cnaddabl 19778 zaddablx 19781 cncrng 21166 cnlmod 24887 pjthlem1 25185 ptolemy 26242 bcp1ctr 27018 cnaddabloOLD 30101 pjhthlem1 30911 gg-cncrng 35486 dnibndlem5 35661 mblfinlem2 36829 facp2 41265 fac2xp3 41326 2xp3dxp2ge1d 41328 factwoffsmonot 41329 mogoldbblem 46686 nnsgrp 46853 nn0mnd 46855 2zrngasgrp 46926 |
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