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Mirrors > Home > MPE Home > Th. List > 2alimi | Structured version Visualization version 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 1739 | . 2 ⊢ (∀𝑦𝜑 → ∀𝑦𝜓) |
3 | 2 | alimi 1739 | 1 ⊢ (∀𝑥∀𝑦𝜑 → ∀𝑥∀𝑦𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1481 |
This theorem was proved from axioms: ax-mp 5 ax-gen 1722 ax-4 1737 |
This theorem is referenced by: 2mo 2551 2eu6 2558 euind 3393 reuind 3411 sbnfc2 4007 opelopabt 4987 ssrel 5207 ssrelOLD 5208 ssrelrel 5220 fundif 5935 opabbrex 6695 fnoprabg 6761 tz7.48lem 7536 ssrelf 29425 bj-3exbi 32600 bj-mo3OLD 32832 mpt2bi123f 33971 mptbi12f 33975 ismrc 37264 refimssco 37913 19.33-2 38581 pm11.63 38595 pm11.71 38597 axc5c4c711to11 38606 |
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