Metamath Proof Explorer

Theorem xaddlid

Description: Extended real version of addlid . (Contributed by Mario Carneiro, 20-Aug-2015)

Ref Expression
Assertion xaddlid 
|- ( A e. RR* -> ( 0 +e A ) = A )

Proof

Step Hyp Ref Expression
1 0xr 
 |-  0 e. RR*
2 xaddcom 
 |-  ( ( 0 e. RR* /\ A e. RR* ) -> ( 0 +e A ) = ( A +e 0 ) )
3 1 2 mpan 
 |-  ( A e. RR* -> ( 0 +e A ) = ( A +e 0 ) )
4 xaddrid 
 |-  ( A e. RR* -> ( A +e 0 ) = A )
5 3 4 eqtrd 
 |-  ( A e. RR* -> ( 0 +e A ) = A )