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Theorem mulcomli 7977
Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.)
Hypotheses
Ref Expression
axi.1 𝐴 ∈ ℂ
axi.2 𝐵 ∈ ℂ
mulcomli.3 (𝐴 · 𝐵) = 𝐶
Assertion
Ref Expression
mulcomli (𝐵 · 𝐴) = 𝐶

Proof of Theorem mulcomli
StepHypRef Expression
1 axi.2 . . 3 𝐵 ∈ ℂ
2 axi.1 . . 3 𝐴 ∈ ℂ
31, 2mulcomi 7976 . 2 (𝐵 · 𝐴) = (𝐴 · 𝐵)
4 mulcomli.3 . 2 (𝐴 · 𝐵) = 𝐶
53, 4eqtri 2208 1 (𝐵 · 𝐴) = 𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1363  wcel 2158  (class class class)co 5888  cc 7822   · cmul 7829
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1457  ax-gen 1459  ax-4 1520  ax-17 1536  ax-ext 2169  ax-mulcom 7925
This theorem depends on definitions:  df-bi 117  df-cleq 2180
This theorem is referenced by:  nummul2c  9446  halfthird  9539  5recm6rec  9540  sq4e2t8  10631  cos2bnd  11781  2lgsoddprmlem3c  14728  2lgsoddprmlem3d  14729  ex-exp  14750  ex-fac  14751
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