Description: Raising a number to the fourth power is equivalent to squaring it twice. (Contributed by SN, 21-Aug-2024)
Ref | Expression | ||
---|---|---|---|
Hypothesis | flt4lem.a | |- ( ph -> A e. CC ) |
|
Assertion | flt4lem | |- ( ph -> ( A ^ 4 ) = ( ( A ^ 2 ) ^ 2 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | flt4lem.a | |- ( ph -> A e. CC ) |
|
2 | 2t2e4 | |- ( 2 x. 2 ) = 4 |
|
3 | 2 | oveq2i | |- ( A ^ ( 2 x. 2 ) ) = ( A ^ 4 ) |
4 | 2nn0 | |- 2 e. NN0 |
|
5 | 4 | a1i | |- ( ph -> 2 e. NN0 ) |
6 | 1 5 5 | expmuld | |- ( ph -> ( A ^ ( 2 x. 2 ) ) = ( ( A ^ 2 ) ^ 2 ) ) |
7 | 3 6 | eqtr3id | |- ( ph -> ( A ^ 4 ) = ( ( A ^ 2 ) ^ 2 ) ) |