Metamath Proof Explorer


Theorem ackfnnn0

Description: The Ackermann function at any nonnegative integer is a function on the nonnegative integers. (Contributed by AV, 4-May-2024) (Proof shortened by AV, 8-May-2024)

Ref Expression
Assertion ackfnnn0 M 0 Ack M Fn 0

Proof

Step Hyp Ref Expression
1 ackendofnn0 M 0 Ack M : 0 0
2 ffn Ack M : 0 0 Ack M Fn 0
3 1 2 syl M 0 Ack M Fn 0