Metamath Proof Explorer


Theorem divcli

Description: Closure law for division. (Contributed by NM, 2-Feb-1995) (Revised by Mario Carneiro, 17-Feb-2014)

Ref Expression
Hypotheses divclz.1
|- A e. CC
divclz.2
|- B e. CC
divcl.3
|- B =/= 0
Assertion divcli
|- ( A / B ) e. CC

Proof

Step Hyp Ref Expression
1 divclz.1
 |-  A e. CC
2 divclz.2
 |-  B e. CC
3 divcl.3
 |-  B =/= 0
4 1 2 divclzi
 |-  ( B =/= 0 -> ( A / B ) e. CC )
5 3 4 ax-mp
 |-  ( A / B ) e. CC