Metamath Proof Explorer


Theorem gcdcld

Description: Closure of the gcd operator. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypotheses gcdcld.1 φM
gcdcld.2 φN
Assertion gcdcld φMgcdN0

Proof

Step Hyp Ref Expression
1 gcdcld.1 φM
2 gcdcld.2 φN
3 gcdcl MNMgcdN0
4 1 2 3 syl2anc φMgcdN0