Theorem addcomi 7906

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 7899	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A + B ) = ( B + A ) )
4	1, 2, 3	mp2an 422	1 |- ( A + B ) = ( B + A )

Syntax hints:   = wceq 1331   e. wcel 1480  (class class class)co 5774   CCcc 7618   + caddc 7623

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-addcom 7720

This theorem is referenced by:  addcomli  7907  add42i  7928  mvlladdi  7980  3m1e2  8840  fztpval  9863  fzo0to42pr  9997  ef01bndlem  11463  tangtx  12919