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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-hbalt | GIF version |
Description: Closed form of hbal 1421 (copied from set.mm). (Contributed by BJ, 2-May-2019.) |
Ref | Expression |
---|---|
bj-hbalt | ⊢ (∀𝑦(𝜑 → ∀𝑥𝜑) → (∀𝑦𝜑 → ∀𝑥∀𝑦𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alim 1401 | . 2 ⊢ (∀𝑦(𝜑 → ∀𝑥𝜑) → (∀𝑦𝜑 → ∀𝑦∀𝑥𝜑)) | |
2 | ax-7 1392 | . 2 ⊢ (∀𝑦∀𝑥𝜑 → ∀𝑥∀𝑦𝜑) | |
3 | 1, 2 | syl6 33 | 1 ⊢ (∀𝑦(𝜑 → ∀𝑥𝜑) → (∀𝑦𝜑 → ∀𝑥∀𝑦𝜑)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1297 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-5 1391 ax-7 1392 |
This theorem is referenced by: bj-nfalt 12553 |
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