Description: Value of the less-than relation. (Contributed by Mario Carneiro, 8-Feb-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | pltval.l | |
|
pltval.s | |
||
Assertion | pltfval | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pltval.l | |
|
2 | pltval.s | |
|
3 | elex | |
|
4 | fveq2 | |
|
5 | 4 1 | eqtr4di | |
6 | 5 | difeq1d | |
7 | df-plt | |
|
8 | 1 | fvexi | |
9 | 8 | difexi | |
10 | 6 7 9 | fvmpt | |
11 | 3 10 | syl | |
12 | 2 11 | eqtrid | |