Metamath Proof Explorer

Theorem pncan3i

Description: Subtraction and addition of equals. (Contributed by NM, 26-Nov-1994)

Ref Expression
Hypotheses negidi.1 
|- A e. CC
pncan3i.2 
|- B e. CC
Assertion pncan3i 
|- ( A + ( B - A ) ) = B

Proof

Step Hyp Ref Expression
1 negidi.1 
 |-  A e. CC
2 pncan3i.2 
 |-  B e. CC
3 pncan3 
 |-  ( ( A e. CC /\ B e. CC ) -> ( A + ( B - A ) ) = B )
4 1 2 3 mp2an 
 |-  ( A + ( B - A ) ) = B