Metamath Proof Explorer


Theorem ackval42a

Description: The Ackermann function at (4,2), expressed with powers of 2. (Contributed by AV, 9-May-2024)

Ref Expression
Assertion ackval42a Could not format assertion : No typesetting found for |- ( ( Ack ` 4 ) ` 2 ) = ( ( 2 ^ ( 2 ^ ( 2 ^ ( 2 ^ 2 ) ) ) ) - 3 ) with typecode |-

Proof

Step Hyp Ref Expression
1 ackval42 Could not format ( ( Ack ` 4 ) ` 2 ) = ( ( 2 ^ ; ; ; ; 6 5 5 3 6 ) - 3 ) : No typesetting found for |- ( ( Ack ` 4 ) ` 2 ) = ( ( 2 ^ ; ; ; ; 6 5 5 3 6 ) - 3 ) with typecode |-
2 sq2 2 2 = 4
3 2 oveq2i 2 2 2 = 2 4
4 2exp4 2 4 = 16
5 3 4 eqtri 2 2 2 = 16
6 5 oveq2i 2 2 2 2 = 2 16
7 2exp16 2 16 = 65536
8 6 7 eqtr2i 65536 = 2 2 2 2
9 8 oveq2i 2 65536 = 2 2 2 2 2
10 9 oveq1i 2 65536 3 = 2 2 2 2 2 3
11 1 10 eqtri Could not format ( ( Ack ` 4 ) ` 2 ) = ( ( 2 ^ ( 2 ^ ( 2 ^ ( 2 ^ 2 ) ) ) ) - 3 ) : No typesetting found for |- ( ( Ack ` 4 ) ` 2 ) = ( ( 2 ^ ( 2 ^ ( 2 ^ ( 2 ^ 2 ) ) ) ) - 3 ) with typecode |-