Metamath Proof Explorer

Theorem dividd

Description: A number divided by itself is one. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses div1d.1 
|- ( ph -> A e. CC )
reccld.2 
|- ( ph -> A =/= 0 )
Assertion dividd 
|- ( ph -> ( A / A ) = 1 )

Proof

Step Hyp Ref Expression
1 div1d.1 
 |-  ( ph -> A e. CC )
2 reccld.2 
 |-  ( ph -> A =/= 0 )
3 divid 
 |-  ( ( A e. CC /\ A =/= 0 ) -> ( A / A ) = 1 )
4 1 2 3 syl2anc 
 |-  ( ph -> ( A / A ) = 1 )