Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-bnj15 | Structured version Visualization version GIF version |
Description: Define the following predicate: 𝑅 is both well-founded and set-like on 𝐴. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-bnj15 | ⊢ (𝑅 FrSe 𝐴 ↔ (𝑅 Fr 𝐴 ∧ 𝑅 Se 𝐴)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | cR | . . 3 class 𝑅 | |
3 | 1, 2 | w-bnj15 32667 | . 2 wff 𝑅 FrSe 𝐴 |
4 | 1, 2 | wfr 5542 | . . 3 wff 𝑅 Fr 𝐴 |
5 | 1, 2 | w-bnj13 32665 | . . 3 wff 𝑅 Se 𝐴 |
6 | 4, 5 | wa 396 | . 2 wff (𝑅 Fr 𝐴 ∧ 𝑅 Se 𝐴) |
7 | 3, 6 | wb 205 | 1 wff (𝑅 FrSe 𝐴 ↔ (𝑅 Fr 𝐴 ∧ 𝑅 Se 𝐴)) |
Colors of variables: wff setvar class |
This definition is referenced by: bnj93 32839 bnj1177 32982 bnj1364 33004 bnj1417 33017 |
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