Metamath Proof Explorer

Theorem mulid1d

Description: Identity law for multiplication. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypothesis addcld.1 
|- ( ph -> A e. CC )
Assertion mulid1d 
|- ( ph -> ( A x. 1 ) = A )

Proof

Step Hyp Ref Expression
1 addcld.1 
 |-  ( ph -> A e. CC )
2 mulid1 
 |-  ( A e. CC -> ( A x. 1 ) = A )
3 1 2 syl 
 |-  ( ph -> ( A x. 1 ) = A )