Description: The gcd operator is commutative, deduction version. (Contributed by SN, 24-Aug-2024)
Ref | Expression | ||
---|---|---|---|
Hypotheses | gcdcomd.m | |- ( ph -> M e. ZZ ) |
|
gcdcomd.n | |- ( ph -> N e. ZZ ) |
||
Assertion | gcdcomd | |- ( ph -> ( M gcd N ) = ( N gcd M ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | gcdcomd.m | |- ( ph -> M e. ZZ ) |
|
2 | gcdcomd.n | |- ( ph -> N e. ZZ ) |
|
3 | gcdcom | |- ( ( M e. ZZ /\ N e. ZZ ) -> ( M gcd N ) = ( N gcd M ) ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> ( M gcd N ) = ( N gcd M ) ) |