Metamath Proof Explorer


Theorem xle0neg1

Description: Extended real version of le0neg1 . (Contributed by Mario Carneiro, 9-Sep-2015)

Ref Expression
Assertion xle0neg1 A * A 0 0 A

Proof

Step Hyp Ref Expression
1 0xr 0 *
2 xleneg A * 0 * A 0 0 A
3 1 2 mpan2 A * A 0 0 A
4 xneg0 0 = 0
5 4 breq1i 0 A 0 A
6 3 5 bitrdi A * A 0 0 A