![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > df-pss | GIF version |
Description: Define proper subclass relationship between two classes. Definition 5.9 of [TakeutiZaring] p. 17. Note that ¬ A ⊊ A (proved in pssirr 3038). Contrast this relationship with the relationship A ⊆ B (as defined in df-ss 2925). Other possible definitions are given by dfpss2 3023 and dfpss3 3024. (Contributed by NM, 7-Feb-1996.) |
Ref | Expression |
---|---|
df-pss | ⊢ (A ⊊ B ↔ (A ⊆ B ∧ A ≠ B)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class A | |
2 | cB | . . 3 class B | |
3 | 1, 2 | wpss 2912 | . 2 wff A ⊊ B |
4 | 1, 2 | wss 2911 | . . 3 wff A ⊆ B |
5 | 1, 2 | wne 2201 | . . 3 wff A ≠ B |
6 | 4, 5 | wa 97 | . 2 wff (A ⊆ B ∧ A ≠ B) |
7 | 3, 6 | wb 98 | 1 wff (A ⊊ B ↔ (A ⊆ B ∧ A ≠ B)) |
Colors of variables: wff set class |
This definition is referenced by: dfpss2 3023 psseq1 3025 psseq2 3026 pssss 3033 pssne 3034 nssinpss 3163 0pss 3259 difsnpssim 3498 |
Copyright terms: Public domain | W3C validator |