Metamath Proof Explorer


Theorem int-mulsimpd

Description: MultiplicationSimplification generator rule. (Contributed by Stanislas Polu, 7-Apr-2020)

Ref Expression
Hypotheses int-mulsimpd.1 φ B
int-mulsimpd.2 φ A = B
int-mulsimpd.3 φ B 0
Assertion int-mulsimpd φ 1 = A B

Proof

Step Hyp Ref Expression
1 int-mulsimpd.1 φ B
2 int-mulsimpd.2 φ A = B
3 int-mulsimpd.3 φ B 0
4 1 recnd φ B
5 4 3 2 diveq1bd φ A B = 1
6 5 eqcomd φ 1 = A B