Metamath Proof Explorer


Theorem int-mulassocd

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

Ref Expression
Hypotheses int-mulassocd.1 φ B
int-mulassocd.2 φ C
int-mulassocd.3 φ D
int-mulassocd.4 φ A = B
Assertion int-mulassocd φ B C D = A C D

Proof

Step Hyp Ref Expression
1 int-mulassocd.1 φ B
2 int-mulassocd.2 φ C
3 int-mulassocd.3 φ D
4 int-mulassocd.4 φ A = B
5 1 recnd φ B
6 2 recnd φ C
7 3 recnd φ D
8 5 6 7 mulassd φ B C D = B C D
9 4 eqcomd φ B = A
10 9 oveq1d φ B C = A C
11 10 oveq1d φ B C D = A C D
12 8 11 eqtr3d φ B C D = A C D