Description: "Less than or equal to" in terms of "less than". ( sspss analog.) (Contributed by NM, 17-Oct-2011) (Revised by Mario Carneiro, 8-Feb-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | pleval2.b | |
|
pleval2.l | |
||
pleval2.s | |
||
Assertion | pleval2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pleval2.b | |
|
2 | pleval2.l | |
|
3 | pleval2.s | |
|
4 | 1 2 3 | pleval2i | |
5 | 4 | 3adant1 | |
6 | 2 3 | pltle | |
7 | 1 2 | posref | |
8 | 7 | 3adant3 | |
9 | breq2 | |
|
10 | 8 9 | syl5ibcom | |
11 | 6 10 | jaod | |
12 | 5 11 | impbid | |