Theorem zmulcld

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

	Ref	Expression
Hypotheses	zred.1	|- ( ph -> A e. ZZ )
	zaddcld.1	|- ( ph -> B e. ZZ )
Assertion	zmulcld	|- ( ph -> ( A x. B ) e. ZZ )

Proof

Step	Hyp	Ref	Expression
1		zred.1	|- ( ph -> A e. ZZ )
2		zaddcld.1	|- ( ph -> B e. ZZ )
3		zmulcl	|- ( ( A e. ZZ /\ B e. ZZ ) -> ( A x. B ) e. ZZ )
4	1 2 3	syl2anc	|- ( ph -> ( A x. B ) e. ZZ )