Metamath Proof Explorer


Theorem nndivdvdsd

Description: A positive integer divides a natural number if and only if the quotient is a positive integer, a deduction version of nndivdvds . (Contributed by metakunt, 12-May-2024)

Ref Expression
Hypotheses nndivdvdsd.1 φ M
nndivdvdsd.2 φ N
Assertion nndivdvdsd φ M N N M

Proof

Step Hyp Ref Expression
1 nndivdvdsd.1 φ M
2 nndivdvdsd.2 φ N
3 nndivdvds N M M N N M
4 2 1 3 syl2anc φ M N N M