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
divclz.2 B
Assertion divclzi B 0 A B

Proof

Step Hyp Ref Expression
1 divclz.1 A
2 divclz.2 B
3 divcl A B B 0 A B
4 1 2 3 mp3an12 B 0 A B