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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-he | Structured version Visualization version GIF version |
Description: The property of relation 𝑅 being hereditary in class 𝐴. (Contributed by RP, 27-Mar-2020.) |
Ref | Expression |
---|---|
df-he | ⊢ (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | cR | . . 3 class 𝑅 | |
3 | 1, 2 | whe 43037 | . 2 wff 𝑅 hereditary 𝐴 |
4 | 2, 1 | cima 5670 | . . 3 class (𝑅 “ 𝐴) |
5 | 4, 1 | wss 3941 | . 2 wff (𝑅 “ 𝐴) ⊆ 𝐴 |
6 | 3, 5 | wb 205 | 1 wff (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴) |
Colors of variables: wff setvar class |
This definition is referenced by: dfhe2 43039 dfhe3 43040 heeq12 43041 sbcheg 43044 hess 43045 xphe 43046 0he 43047 he0 43049 unhe1 43050 snhesn 43051 dffrege76 43204 |
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