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Theorem mulcomli 7592
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 7591 . 2 (𝐵 · 𝐴) = (𝐴 · 𝐵)
4 mulcomli.3 . 2 (𝐴 · 𝐵) = 𝐶
53, 4eqtri 2115 1 (𝐵 · 𝐴) = 𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1296  wcel 1445  (class class class)co 5690  cc 7445   · cmul 7452
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1388  ax-gen 1390  ax-4 1452  ax-17 1471  ax-ext 2077  ax-mulcom 7543
This theorem depends on definitions:  df-bi 116  df-cleq 2088
This theorem is referenced by:  nummul2c  9025  sq4e2t8  10167  cos2bnd  11200  ex-exp  12371  ex-fac  12372
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