Metamath Proof Explorer

Theorem mul01d

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 mul01d 
|- ( ph -> ( A x. 0 ) = 0 )

Proof

Step Hyp Ref Expression
1 muld.1 
 |-  ( ph -> A e. CC )
2 mul01 
 |-  ( A e. CC -> ( A x. 0 ) = 0 )
3 1 2 syl 
 |-  ( ph -> ( A x. 0 ) = 0 )