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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 43785 | . 2 wff 𝑅 hereditary 𝐴 |
| 4 | 2, 1 | cima 5688 | . . 3 class (𝑅 “ 𝐴) |
| 5 | 4, 1 | wss 3951 | . 2 wff (𝑅 “ 𝐴) ⊆ 𝐴 |
| 6 | 3, 5 | wb 206 | 1 wff (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴) |
| Colors of variables: wff setvar class |
| This definition is referenced by: dfhe2 43787 dfhe3 43788 heeq12 43789 sbcheg 43792 hess 43793 xphe 43794 0he 43795 he0 43797 unhe1 43798 snhesn 43799 dffrege76 43952 |
| Copyright terms: Public domain | W3C validator |