Metamath Proof Explorer


Theorem mul02i

Description: Multiplication by 0. Theorem I.6 of Apostol p. 18. (Contributed by NM, 23-Nov-1994)

Ref Expression
Hypothesis mul.1
|- A e. CC
Assertion mul02i
|- ( 0 x. A ) = 0

Proof

Step Hyp Ref Expression
1 mul.1
 |-  A e. CC
2 mul02
 |-  ( A e. CC -> ( 0 x. A ) = 0 )
3 1 2 ax-mp
 |-  ( 0 x. A ) = 0