Metamath Proof Explorer

Theorem mul02d

Description: Multiplication by 0. Theorem I.6 of Apostol p. 18. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypothesis muld.1 
|- ( ph -> A e. CC )
Assertion mul02d 
|- ( ph -> ( 0 x. A ) = 0 )

Proof

Step Hyp Ref Expression
1 muld.1 
 |-  ( ph -> A e. CC )
2 mul02 
 |-  ( A e. CC -> ( 0 x. A ) = 0 )
3 1 2 syl 
 |-  ( ph -> ( 0 x. A ) = 0 )