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Theorem 2alanimi 37490
Description: Removes two universal quantifiers from a statement. (Contributed by Andrew Salmon, 24-May-2011.)
Hypothesis
Ref Expression
2alanimi.1 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
2alanimi ((∀𝑥𝑦𝜑 ∧ ∀𝑥𝑦𝜓) → ∀𝑥𝑦𝜒)

Proof of Theorem 2alanimi
StepHypRef Expression
1 2alanimi.1 . . 3 ((𝜑𝜓) → 𝜒)
21alanimi 1719 . 2 ((∀𝑦𝜑 ∧ ∀𝑦𝜓) → ∀𝑦𝜒)
32alanimi 1719 1 ((∀𝑥𝑦𝜑 ∧ ∀𝑥𝑦𝜓) → ∀𝑥𝑦𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  wal 1472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1700  ax-4 1713
This theorem depends on definitions:  df-bi 195  df-an 384
This theorem is referenced by: (None)
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