Description: The absolute value of a real number is either that number or its negative. (Contributed by Mario Carneiro, 29-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypothesis | resqrcld.1 | |- ( ph -> A e. RR ) |
|
Assertion | absord | |- ( ph -> ( ( abs ` A ) = A \/ ( abs ` A ) = -u A ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resqrcld.1 | |- ( ph -> A e. RR ) |
|
2 | absor | |- ( A e. RR -> ( ( abs ` A ) = A \/ ( abs ` A ) = -u A ) ) |
|
3 | 1 2 | syl | |- ( ph -> ( ( abs ` A ) = A \/ ( abs ` A ) = -u A ) ) |