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Mirrors > Home > MPE Home > Th. List > addass | Structured version Visualization version GIF version |
Description: Alias for ax-addass 11181, for naming consistency with addassi 11231. (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 11181 | 1 ⊢ ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ∧ 𝐶 ∈ ℂ) → ((𝐴 + 𝐵) + 𝐶) = (𝐴 + (𝐵 + 𝐶))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1086 = wceq 1540 ∈ wcel 2105 (class class class)co 7412 ℂcc 11114 + caddc 11119 |
This theorem was proved from axioms: ax-addass 11181 |
This theorem is referenced by: addassi 11231 addassd 11243 00id 11396 addlid 11404 add12 11438 add32 11439 add32r 11440 add4 11441 nnaddcl 12242 uzaddcl 12895 xaddass 13235 fztp 13564 seradd 14017 expadd 14077 bernneq 14199 faclbnd6 14266 hashgadd 14344 swrds2 14898 clim2ser 15608 clim2ser2 15609 summolem3 15667 isumsplit 15793 fsumcube 16011 odd2np1lem 16290 prmlem0 17046 cnaddablx 19784 cnaddabl 19785 zaddablx 19788 cncrng 21255 cnlmod 24987 pjthlem1 25285 ptolemy 26346 bcp1ctr 27126 cnaddabloOLD 30268 pjhthlem1 31078 gg-cncrng 35649 dnibndlem5 35824 mblfinlem2 36992 facp2 41428 fac2xp3 41489 2xp3dxp2ge1d 41491 factwoffsmonot 41492 mogoldbblem 46849 nnsgrp 47016 nn0mnd 47018 2zrngasgrp 47085 |
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