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Theorem 2alimdv 1834
Description: Deduction form of Theorem 19.20 of [Margaris] p. 90 with two quantifiers, see alim 1729. (Contributed by NM, 27-Apr-2004.)
Hypothesis
Ref Expression
2alimdv.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
2alimdv (𝜑 → (∀𝑥𝑦𝜓 → ∀𝑥𝑦𝜒))
Distinct variable groups:   𝜑,𝑥   𝜑,𝑦
Allowed substitution hints:   𝜓(𝑥,𝑦)   𝜒(𝑥,𝑦)

Proof of Theorem 2alimdv
StepHypRef Expression
1 2alimdv.1 . . 3 (𝜑 → (𝜓𝜒))
21alimdv 1832 . 2 (𝜑 → (∀𝑦𝜓 → ∀𝑦𝜒))
32alimdv 1832 1 (𝜑 → (∀𝑥𝑦𝜓 → ∀𝑥𝑦𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1473
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1713  ax-4 1728  ax-5 1827
This theorem is referenced by:  soss  4967  dfwe2  6851  tz7.48lem  7401  ss2mcls  30513  mclsax  30514
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