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Theorem 2alimi 1456
Description: Inference doubly quantifying both antecedent and consequent. (Contributed by NM, 3-Feb-2005.)
Hypothesis
Ref Expression
alimi.1 (𝜑𝜓)
Assertion
Ref Expression
2alimi (∀𝑥𝑦𝜑 → ∀𝑥𝑦𝜓)

Proof of Theorem 2alimi
StepHypRef Expression
1 alimi.1 . . 3 (𝜑𝜓)
21alimi 1455 . 2 (∀𝑦𝜑 → ∀𝑦𝜓)
32alimi 1455 1 (∀𝑥𝑦𝜑 → ∀𝑥𝑦𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1351
This theorem was proved from axioms:  ax-mp 5  ax-5 1447  ax-gen 1449
This theorem is referenced by:  mo23  2067  mo3h  2079  spc2gv  2828  spc3gv  2830  euind  2924  reuind  2942  sbnfc2  3117  opelopabt  4262  ssrel  4714  ssrelrel  4726  fnoprabg  5975
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