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Theorem addcomi 7371
Description: Addition commutes. Based on ideas by Eric Schmidt. (Contributed by Scott Fenton, 3-Jan-2013.)
Hypotheses
Ref Expression
mul.1  |-  A  e.  CC
mul.2  |-  B  e.  CC
Assertion
Ref Expression
addcomi  |-  ( A  +  B )  =  ( B  +  A
)

Proof of Theorem addcomi
StepHypRef Expression
1 mul.1 . 2  |-  A  e.  CC
2 mul.2 . 2  |-  B  e.  CC
3 addcom 7364 . 2  |-  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  +  B
)  =  ( B  +  A ) )
41, 2, 3mp2an 417 1  |-  ( A  +  B )  =  ( B  +  A
)
Colors of variables: wff set class
Syntax hints:    = wceq 1285    e. wcel 1434  (class class class)co 5563   CCcc 7093    + caddc 7098
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106  ax-addcom 7190
This theorem is referenced by:  addcomli  7372  add42i  7393  mvlladdi  7445  3m1e2  8277  fztpval  9228  fzo0to42pr  9358
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