Theorem addcomi 8472

Description: Addition is commutative. 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

Step	Hyp	Ref	Expression
1		mul.1	. 2 |- A e. CC
2		mul.2	. 2 |- B e. CC
3		addcom 8465	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A + B ) = ( B + A ) )
4	1, 2, 3	mp2an 430	1 |- ( A + B ) = ( B + A )

This proof depends on syntax axioms:   = wceq 1402   e. wcel 2209  (class class class)co 6085   CCcc 8178   + caddc 8183

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-addcom 8280

This theorem is used by:  addcomli  8473  add42i  8494  mvlladdi  8546  3m1e2  9427  fztpval  10501  fzo0to42pr  10649  ef01bndlem  12541  modxai  13217  tangtx  15992  log2ublem2  16144  ppiqub  16215  lgsdir2lem2  16270  lgsdir2lem3  16271  lgsdir2lem5  16273