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Mirrors > Home > NFE 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 1559 | . 2 ⊢ (∀yφ → ∀yψ) |
3 | 2 | alimi 1559 | 1 ⊢ (∀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-gen 1546 ax-5 1557 |
This theorem is referenced by: mo 2226 2mo 2282 2eu6 2289 euind 3023 reuind 3039 sbnfc2 3196 spfininduct 4540 opelopabt 4699 fvopab4t 5385 fnoprabg 5585 |
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