Description: The nonnegative extended reals are closed under multiplication. (Contributed by Mario Carneiro, 26-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | ge0xmulcl | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elxrge0 | |
|
2 | elxrge0 | |
|
3 | xmulcl | |
|
4 | 3 | ad2ant2r | |
5 | xmulge0 | |
|
6 | elxrge0 | |
|
7 | 4 5 6 | sylanbrc | |
8 | 1 2 7 | syl2anb | |