Description: Deduction form of binom2. (Contributed by Igor Ieskov, 14-Dec-2023)
Ref | Expression | ||
---|---|---|---|
Hypotheses | binom2d.1 | |- ( ph -> A e. CC ) |
|
binom2d.2 | |- ( ph -> B e. CC ) |
||
Assertion | binom2d | |- ( ph -> ( ( A + B ) ^ 2 ) = ( ( ( A ^ 2 ) + ( 2 x. ( A x. B ) ) ) + ( B ^ 2 ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | binom2d.1 | |- ( ph -> A e. CC ) |
|
2 | binom2d.2 | |- ( ph -> B e. CC ) |
|
3 | binom2 | |- ( ( A e. CC /\ B e. CC ) -> ( ( A + B ) ^ 2 ) = ( ( ( A ^ 2 ) + ( 2 x. ( A x. B ) ) ) + ( B ^ 2 ) ) ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> ( ( A + B ) ^ 2 ) = ( ( ( A ^ 2 ) + ( 2 x. ( A x. B ) ) ) + ( B ^ 2 ) ) ) |