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Theorem 2alimdv 1803
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (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 1801 . 2 (𝜑 → (∀𝑦𝜓 → ∀𝑦𝜒))
32alimdv 1801 1 (𝜑 → (∀𝑥𝑦𝜓 → ∀𝑥𝑦𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1283
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1377  ax-gen 1379  ax-17 1460
This theorem is referenced by:  moimv  2008  soss  4077
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