Theorem binom2d

Description: Deduction form of binom2 . (Contributed by Igor Ieskov, 14-Dec-2023)

	Ref	Expression
Hypotheses	binom2d.1	|- ( ph -> A e. CC )
	binom2d.2	|- ( ph -> B e. CC )
Assertion	binom2d	|- ( ph -> ( ( A + B ) ^ 2 ) = ( ( ( A ^ 2 ) + ( 2 x. ( A x. B ) ) ) + ( B ^ 2 ) ) )

Proof

Step	Hyp	Ref	Expression
1		binom2d.1	|- ( ph -> A e. CC )
2		binom2d.2	|- ( ph -> B e. CC )
3		binom2	|- ( ( A e. CC /\ B e. CC ) -> ( ( A + B ) ^ 2 ) = ( ( ( A ^ 2 ) + ( 2 x. ( A x. B ) ) ) + ( B ^ 2 ) ) )
4	1 2 3	syl2anc	|- ( ph -> ( ( A + B ) ^ 2 ) = ( ( ( A ^ 2 ) + ( 2 x. ( A x. B ) ) ) + ( B ^ 2 ) ) )