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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdsep1 | GIF version |
Description: Version of ax-bdsep 14518 without initial universal quantifier. (Contributed by BJ, 5-Oct-2019.) |
Ref | Expression |
---|---|
bdsep1.1 | ⊢ BOUNDED 𝜑 |
Ref | Expression |
---|---|
bdsep1 | ⊢ ∃𝑏∀𝑥(𝑥 ∈ 𝑏 ↔ (𝑥 ∈ 𝑎 ∧ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdsep1.1 | . . 3 ⊢ BOUNDED 𝜑 | |
2 | 1 | ax-bdsep 14518 | . 2 ⊢ ∀𝑎∃𝑏∀𝑥(𝑥 ∈ 𝑏 ↔ (𝑥 ∈ 𝑎 ∧ 𝜑)) |
3 | 2 | spi 1536 | 1 ⊢ ∃𝑏∀𝑥(𝑥 ∈ 𝑏 ↔ (𝑥 ∈ 𝑎 ∧ 𝜑)) |
Colors of variables: wff set class |
Syntax hints: ∧ wa 104 ↔ wb 105 ∀wal 1351 ∃wex 1492 BOUNDED wbd 14446 |
This theorem was proved from axioms: ax-mp 5 ax-4 1510 ax-bdsep 14518 |
This theorem is referenced by: bdsep2 14520 bdzfauscl 14524 bdbm1.3ii 14525 bj-axemptylem 14526 bj-nalset 14529 |
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