Theorem binom2d

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

	Ref	Expression
Hypotheses	binom2d.1	$$⊢\phi \to A\in ℂ$$
	binom2d.2	$$⊢\phi \to B\in ℂ$$
Assertion	binom2d	$$⊢\phi \to {\left(A+B\right)}^2=A^2+2AB+B^2$$

Proof

Step	Hyp	Ref	Expression
1		binom2d.1	$$⊢\phi \to A\in ℂ$$
2		binom2d.2	$$⊢\phi \to B\in ℂ$$
3		binom2	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to {\left(A+B\right)}^2=A^2+2AB+B^2$$
4	1 2 3	syl2anc	$$⊢\phi \to {\left(A+B\right)}^2=A^2+2AB+B^2$$