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	Could not format assertion : No typesetting found for |- ( M e. NN0 -> ( Ack ` M ) Fn NN0 ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		ackendofnn0	Could not format ( M e. NN0 -> ( Ack ` M ) : NN0 --> NN0 ) : No typesetting found for |- ( M e. NN0 -> ( Ack ` M ) : NN0 --> NN0 ) with typecode |-
2		ffn	Could not format ( ( Ack ` M ) : NN0 --> NN0 -> ( Ack ` M ) Fn NN0 ) : No typesetting found for |- ( ( Ack ` M ) : NN0 --> NN0 -> ( Ack ` M ) Fn NN0 ) with typecode |-
3	1 2	syl	Could not format ( M e. NN0 -> ( Ack ` M ) Fn NN0 ) : No typesetting found for |- ( M e. NN0 -> ( Ack ` M ) Fn NN0 ) with typecode |-