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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-2alim | Structured version Visualization version GIF version |
Description: Closed form of 2alimi 1819. (Contributed by BJ, 6-May-2019.) |
Ref | Expression |
---|---|
bj-2alim | ⊢ (∀𝑥∀𝑦(𝜑 → 𝜓) → (∀𝑥∀𝑦𝜑 → ∀𝑥∀𝑦𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alim 1817 | . 2 ⊢ (∀𝑦(𝜑 → 𝜓) → (∀𝑦𝜑 → ∀𝑦𝜓)) | |
2 | 1 | al2imi 1822 | 1 ⊢ (∀𝑥∀𝑦(𝜑 → 𝜓) → (∀𝑥∀𝑦𝜑 → ∀𝑥∀𝑦𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-gen 1802 ax-4 1816 |
This theorem is referenced by: (None) |
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