Metamath Proof Explorer


Theorem dec0u

Description: Add a zero in the units place. (Contributed by Mario Carneiro, 17-Apr-2015) (Revised by AV, 6-Sep-2021)

Ref Expression
Hypothesis dec0u.1
|- A e. NN0
Assertion dec0u
|- ( ; 1 0 x. A ) = ; A 0

Proof

Step Hyp Ref Expression
1 dec0u.1
 |-  A e. NN0
2 10nn0
 |-  ; 1 0 e. NN0
3 2 1 num0u
 |-  ( ; 1 0 x. A ) = ( ( ; 1 0 x. A ) + 0 )
4 dfdec10
 |-  ; A 0 = ( ( ; 1 0 x. A ) + 0 )
5 3 4 eqtr4i
 |-  ( ; 1 0 x. A ) = ; A 0