Metamath Proof Explorer


Theorem 0dig1

Description: The 0 th digit of 1 is 1 in any positional system. (Contributed by AV, 28-May-2020)

Ref Expression
Assertion 0dig1 B 2 0 digit B 1 = 1

Proof

Step Hyp Ref Expression
1 0z 0
2 dig1 B 2 0 0 digit B 1 = if 0 = 0 1 0
3 1 2 mpan2 B 2 0 digit B 1 = if 0 = 0 1 0
4 eqid 0 = 0
5 4 iftruei if 0 = 0 1 0 = 1
6 3 5 eqtrdi B 2 0 digit B 1 = 1