Metamath Proof Explorer

Theorem zmulcld

Description: Closure of multiplication of integers. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypotheses zred.1 φ A
zaddcld.1 φ B
Assertion zmulcld φ A B


Step Hyp Ref Expression
1 zred.1 φ A
2 zaddcld.1 φ B
3 zmulcl A B A B
4 1 2 3 syl2anc φ A B