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Theorem mulcomli 7780
Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.)
Hypotheses
Ref Expression
axi.1  |-  A  e.  CC
axi.2  |-  B  e.  CC
mulcomli.3  |-  ( A  x.  B )  =  C
Assertion
Ref Expression
mulcomli  |-  ( B  x.  A )  =  C

Proof of Theorem mulcomli
StepHypRef Expression
1 axi.2 . . 3  |-  B  e.  CC
2 axi.1 . . 3  |-  A  e.  CC
31, 2mulcomi 7779 . 2  |-  ( B  x.  A )  =  ( A  x.  B
)
4 mulcomli.3 . 2  |-  ( A  x.  B )  =  C
53, 4eqtri 2160 1  |-  ( B  x.  A )  =  C
Colors of variables: wff set class
Syntax hints:    = wceq 1331    e. wcel 1480  (class class class)co 5774   CCcc 7625    x. cmul 7632
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-4 1487  ax-17 1506  ax-ext 2121  ax-mulcom 7728
This theorem depends on definitions:  df-bi 116  df-cleq 2132
This theorem is referenced by:  nummul2c  9238  halfthird  9331  5recm6rec  9332  sq4e2t8  10397  cos2bnd  11474  ex-exp  12969  ex-fac  12970
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