Metamath Proof Explorer


Theorem dvdsmultr1d

Description: Deduction form of dvdsmultr1 . (Contributed by Stanislas Polu, 9-Mar-2020)

Ref Expression
Hypotheses dvdsmultr1d.1 φ K
dvdsmultr1d.2 φ M
dvdsmultr1d.3 φ N
dvdsmultr1d.4 φ K M
Assertion dvdsmultr1d φ K M N

Proof

Step Hyp Ref Expression
1 dvdsmultr1d.1 φ K
2 dvdsmultr1d.2 φ M
3 dvdsmultr1d.3 φ N
4 dvdsmultr1d.4 φ K M
5 dvdsmultr1 K M N K M K M N
6 1 2 3 5 syl3anc φ K M K M N
7 4 6 mpd φ K M N