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Theorem addcomi 8024
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 8017 . 2  |-  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  +  B
)  =  ( B  +  A ) )
41, 2, 3mp2an 423 1  |-  ( A  +  B )  =  ( B  +  A
)
Colors of variables: wff set class
Syntax hints:    = wceq 1335    e. wcel 2128  (class class class)co 5827   CCcc 7733    + caddc 7738
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-addcom 7835
This theorem is referenced by:  addcomli  8025  add42i  8046  mvlladdi  8098  3m1e2  8959  fztpval  9992  fzo0to42pr  10129  ef01bndlem  11665  tangtx  13255
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