Metamath Proof Explorer


Theorem resubd

Description: Real part distributes over subtraction. (Contributed by Mario Carneiro, 29-May-2016)

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

Proof

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