Theorem addcomi 8170

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

Step	Hyp	Ref	Expression
1		mul.1	. 2 |- A e. CC
2		mul.2	. 2 |- B e. CC
3		addcom 8163	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A + B ) = ( B + A ) )
4	1, 2, 3	mp2an 426	1 |- ( A + B ) = ( B + A )

Syntax hints:   = wceq 1364   e. wcel 2167  (class class class)co 5922   CCcc 7877   + caddc 7882

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-addcom 7979

This theorem is referenced by:  addcomli  8171  add42i  8192  mvlladdi  8244  3m1e2  9110  fztpval  10158  fzo0to42pr  10296  ef01bndlem  11921  modxai  12585  tangtx  15074  lgsdir2lem2  15270  lgsdir2lem3  15271  lgsdir2lem5  15273