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| Mirrors > Home > MPE Home > Th. List > df-rel | Structured version Visualization version GIF version | ||
| Description: Define the relation predicate. Definition 6.4(1) of [TakeutiZaring] p. 23. For alternate definitions, see dfrel2 6209 and dfrel3 6218. (Contributed by NM, 1-Aug-1994.) |
| Ref | Expression |
|---|---|
| df-rel | ⊢ (Rel 𝐴 ↔ 𝐴 ⊆ (V × V)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cA | . . 3 class 𝐴 | |
| 2 | 1 | wrel 5690 | . 2 wff Rel 𝐴 |
| 3 | cvv 3480 | . . . 4 class V | |
| 4 | 3, 3 | cxp 5683 | . . 3 class (V × V) |
| 5 | 1, 4 | wss 3951 | . 2 wff 𝐴 ⊆ (V × V) |
| 6 | 2, 5 | wb 206 | 1 wff (Rel 𝐴 ↔ 𝐴 ⊆ (V × V)) |
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