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Metamath Proof Explorer

Definition df-fin6

Description: A set is VI-finite iff it behaves finitely under X. . Definition VI of Levy58 p. 4. (Contributed by Stefan O'Rear, 12-Nov-2014)

Ref Expression
Assertion df-fin6 FinVI = { 𝑥 ∣ ( 𝑥 ≺ 2o ∨ 𝑥 ≺ ( 𝑥 × 𝑥 ) ) }

Detailed syntax breakdown

Step Hyp Ref Expression
0 cfin6 ⊢ FinVI
1 vx ⊢ 𝑥
2 1 cv ⊢ 𝑥
3 csdm ⊢ ≺
4 c2o ⊢ 2o
5 2 4 3 wbr ⊢ 𝑥 ≺ 2o
6 2 2 cxp ⊢ ( 𝑥 × 𝑥 )
7 2 6 3 wbr ⊢ 𝑥 ≺ ( 𝑥 × 𝑥 )
8 5 7 wo ⊢ ( 𝑥 ≺ 2o ∨ 𝑥 ≺ ( 𝑥 × 𝑥 ) )
9 8 1 cab ⊢ { 𝑥 ∣ ( 𝑥 ≺ 2o ∨ 𝑥 ≺ ( 𝑥 × 𝑥 ) ) }
10 0 9 wceq ⊢ FinVI = { 𝑥 ∣ ( 𝑥 ≺ 2o ∨ 𝑥 ≺ ( 𝑥 × 𝑥 ) ) }