Theorem addcomi 8163

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 8156	. 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 2164  (class class class)co 5918   CCcc 7870   + caddc 7875

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-addcom 7972

This theorem is referenced by:  addcomli  8164  add42i  8185  mvlladdi  8237  3m1e2  9102  fztpval  10149  fzo0to42pr  10287  ef01bndlem  11899  tangtx  14973  lgsdir2lem2  15145  lgsdir2lem3  15146  lgsdir2lem5  15148