Metamath Proof Explorer


Theorem divne0d

Description: The ratio of nonzero numbers is nonzero. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses div1d.1 φA
divcld.2 φB
divne0d.3 φA0
divne0d.4 φB0
Assertion divne0d φAB0

Proof

Step Hyp Ref Expression
1 div1d.1 φA
2 divcld.2 φB
3 divne0d.3 φA0
4 divne0d.4 φB0
5 divne0 AA0BB0AB0
6 1 3 2 4 5 syl22anc φAB0