Metamath Proof Explorer


Theorem divmul2d

Description: Relationship between division and multiplication. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses div1d.1 φ A
divcld.2 φ B
divmuld.3 φ C
divassd.4 φ C 0
Assertion divmul2d φ A C = B A = C B

Proof

Step Hyp Ref Expression
1 div1d.1 φ A
2 divcld.2 φ B
3 divmuld.3 φ C
4 divassd.4 φ C 0
5 divmul2 A B C C 0 A C = B A = C B
6 1 2 3 4 5 syl112anc φ A C = B A = C B