Theorem sqdivd

Description: Distribution of squaring over division. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypotheses	expcld.1	|- ( ph -> A e. CC )
	mulexpd.2	|- ( ph -> B e. CC )
	sqdivd.3	|- ( ph -> B =/= 0 )
Assertion	sqdivd	|- ( ph -> ( ( A / B ) ^ 2 ) = ( ( A ^ 2 ) / ( B ^ 2 ) ) )

Proof

Step	Hyp	Ref	Expression
1		expcld.1	|- ( ph -> A e. CC )
2		mulexpd.2	|- ( ph -> B e. CC )
3		sqdivd.3	|- ( ph -> B =/= 0 )
4		sqdiv	|- ( ( A e. CC /\ B e. CC /\ B =/= 0 ) -> ( ( A / B ) ^ 2 ) = ( ( A ^ 2 ) / ( B ^ 2 ) ) )
5	1 2 3 4	syl3anc	|- ( ph -> ( ( A / B ) ^ 2 ) = ( ( A ^ 2 ) / ( B ^ 2 ) ) )