Theorem gcdcomd

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 ) )

Proof

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 ) )