Metamath Proof Explorer

Theorem addcomi

Description: Addition commutes. Based on ideas by Eric Schmidt. (Contributed by Scott Fenton, 3-Jan-2013)

Ref Expression
Hypotheses mul.1 
|- A e. CC
mul.2 
|- B e. CC
Assertion addcomi 
|- ( A + B ) = ( B + A )

Proof

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