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Mirrors > Home > ILE Home > Th. List > 2alimi | GIF version |
Description: Inference doubly quantifying both antecedent and consequent. (Contributed by NM, 3-Feb-2005.) |
Ref | Expression |
---|---|
alimi.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
2alimi | ⊢ (∀𝑥∀𝑦𝜑 → ∀𝑥∀𝑦𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alimi.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 1 | alimi 1399 | . 2 ⊢ (∀𝑦𝜑 → ∀𝑦𝜓) |
3 | 2 | alimi 1399 | 1 ⊢ (∀𝑥∀𝑦𝜑 → ∀𝑥∀𝑦𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1297 |
This theorem was proved from axioms: ax-mp 7 ax-5 1391 ax-gen 1393 |
This theorem is referenced by: mo23 2001 mo3h 2013 spc2gv 2731 spc3gv 2733 euind 2824 reuind 2842 sbnfc2 3010 opelopabt 4122 ssrel 4565 ssrelrel 4577 fnoprabg 5804 |
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