Metamath Proof Explorer

Theorem divclzi

Description: Closure law for division. (Contributed by NM, 7-May-1999) (Revised by Mario Carneiro, 17-Feb-2014)

Ref Expression
Hypotheses divclz.1 
|- A e. CC
divclz.2 
|- B e. CC
Assertion divclzi 
|- ( B =/= 0 -> ( A / B ) e. CC )

Proof

Step Hyp Ref Expression
1 divclz.1 
 |-  A e. CC
2 divclz.2 
 |-  B e. CC
3 divcl 
 |-  ( ( A e. CC /\ B e. CC /\ B =/= 0 ) -> ( A / B ) e. CC )
4 1 2 3 mp3an12 
 |-  ( B =/= 0 -> ( A / B ) e. CC )