Metamath Proof Explorer

Theorem xdiv0rp

Description: Division into zero is zero. (Contributed by Thierry Arnoux, 18-Dec-2016)

Ref Expression
Assertion xdiv0rp 
|- ( A e. RR+ -> ( 0 /e A ) = 0 )

Proof

Step Hyp Ref Expression
1 rprene0 
 |-  ( A e. RR+ -> ( A e. RR /\ A =/= 0 ) )
2 xdiv0 
 |-  ( ( A e. RR /\ A =/= 0 ) -> ( 0 /e A ) = 0 )
3 1 2 syl 
 |-  ( A e. RR+ -> ( 0 /e A ) = 0 )