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