Metamath Proof Explorer


Definition df-bnj15

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
Assertion df-bnj15 ( 𝑅 FrSe 𝐴 ↔ ( 𝑅 Fr 𝐴𝑅 Se 𝐴 ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cR 𝑅
1 cA 𝐴
2 1 0 w-bnj15 𝑅 FrSe 𝐴
3 1 0 wfr 𝑅 Fr 𝐴
4 1 0 w-bnj13 𝑅 Se 𝐴
5 3 4 wa ( 𝑅 Fr 𝐴𝑅 Se 𝐴 )
6 2 5 wb ( 𝑅 FrSe 𝐴 ↔ ( 𝑅 Fr 𝐴𝑅 Se 𝐴 ) )