Theorem addcomi 7157

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 7150	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A + B ) = ( B + A ) )
4	1, 2, 3	mp2an 402	1 |- ( A + B ) = ( B + A )

Syntax hints:   = wceq 1243   e. wcel 1393  (class class class)co 5512   CCcc 6887   + caddc 6892

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101  ax-addcom 6984

This theorem is referenced by:  addcomli  7158  add42i  7177  mvlladdi  7229  3m1e2  8036  fztpval  8945  fzo0to42pr  9076