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Theorem mulcomi 7187
Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.)
Hypotheses
Ref Expression
axi.1  |-  A  e.  CC
axi.2  |-  B  e.  CC
Assertion
Ref Expression
mulcomi  |-  ( A  x.  B )  =  ( B  x.  A
)

Proof of Theorem mulcomi
StepHypRef Expression
1 axi.1 . 2  |-  A  e.  CC
2 axi.2 . 2  |-  B  e.  CC
3 mulcom 7164 . 2  |-  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  x.  B
)  =  ( B  x.  A ) )
41, 2, 3mp2an 417 1  |-  ( A  x.  B )  =  ( B  x.  A
)
Colors of variables: wff set class
Syntax hints:    = wceq 1285    e. wcel 1434  (class class class)co 5543   CCcc 7041    x. cmul 7048
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106  ax-mulcom 7139
This theorem is referenced by:  mulcomli  7188  8th4div3  8317  numma2c  8603  nummul2c  8607  9t11e99  8687  binom2i  9680  fac3  9756
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