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Mirrors > Home > ILE Home > Th. List > Mathboxes > ax-bdex | GIF version |
Description: A bounded existential quantification of a bounded formula is bounded. Note the DV condition on x, y. (Contributed by BJ, 25-Sep-2019.) |
Ref | Expression |
---|---|
bdal.1 | ⊢ BOUNDED φ |
Ref | Expression |
---|---|
ax-bdex | ⊢ BOUNDED ∃x ∈ y φ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . . 3 wff φ | |
2 | vx | . . 3 setvar x | |
3 | vy | . . . 4 setvar y | |
4 | 3 | cv 1241 | . . 3 class y |
5 | 1, 2, 4 | wrex 2301 | . 2 wff ∃x ∈ y φ |
6 | 5 | wbd 9267 | 1 wff BOUNDED ∃x ∈ y φ |
Colors of variables: wff set class |
This axiom is referenced by: bj-bdcel 9292 bdreu 9310 bdrmo 9311 bdcuni 9331 bdciun 9333 bj-axun2 9370 bj-nn0suc0 9410 |
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