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Theorem 2alimi 1361
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 1360 . 2 (∀𝑦𝜑 → ∀𝑦𝜓)
32alimi 1360 1 (∀𝑥𝑦𝜑 → ∀𝑥𝑦𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1257
This theorem was proved from axioms:  ax-mp 7  ax-5 1352  ax-gen 1354
This theorem is referenced by:  mo23  1957  mo3h  1969  spc2gv  2660  spc3gv  2662  euind  2751  reuind  2767  sbnfc2  2934  opelopabt  4027  ssrel  4456  ssrelrel  4468  fnoprabg  5630
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