Metamath Proof Explorer

Theorem subcli

Description: Closure law for subtraction. (Contributed by NM, 26-Nov-1994) (Revised by Mario Carneiro, 21-Dec-2013)

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

Proof

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