Metamath Proof Explorer


Theorem recne0d

Description: The reciprocal of a nonzero number is nonzero. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses div1d.1 φA
reccld.2 φA0
Assertion recne0d φ1A0

Proof

Step Hyp Ref Expression
1 div1d.1 φA
2 reccld.2 φA0
3 recne0 AA01A0
4 1 2 3 syl2anc φ1A0