Metamath Proof Explorer


Theorem recne0

Description: The reciprocal of a nonzero number is nonzero. (Contributed by NM, 9-Feb-2006) (Proof shortened by Mario Carneiro, 27-May-2016)

Ref Expression
Assertion recne0 AA01A0

Proof

Step Hyp Ref Expression
1 ax-1cn 1
2 ax-1ne0 10
3 divne0 110AA01A0
4 1 2 3 mpanl12 AA01A0