Metamath Proof Explorer


Theorem immuld

Description: Imaginary part of a product. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypotheses recld.1 φ A
readdd.2 φ B
Assertion immuld φ A B = A B + A B

Proof

Step Hyp Ref Expression
1 recld.1 φ A
2 readdd.2 φ B
3 immul A B A B = A B + A B
4 1 2 3 syl2anc φ A B = A B + A B