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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 1730 | . 2 ⊢ (∀𝑦𝜑 → ∀𝑦𝜓) |
3 | 2 | alimi 1730 | 1 ⊢ (∀𝑥∀𝑦𝜑 → ∀𝑥∀𝑦𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 |
This theorem was proved from axioms: ax-mp 5 ax-gen 1713 ax-4 1728 |
This theorem is referenced by: 2mo 2539 2eu6 2546 euind 3360 reuind 3378 sbnfc2 3959 opelopabt 4912 ssrel 5130 ssrelOLD 5131 ssrelrel 5143 fundif 5849 opabbrex 6593 fnoprabg 6659 tz7.48lem 7423 ssrelf 28805 bj-3exbi 31785 bj-mo3OLD 32022 mpt2bi123f 33141 mptbi12f 33145 ismrc 36282 refimssco 36932 19.33-2 37603 pm11.63 37617 pm11.71 37619 axc5c4c711to11 37628 |
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