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Theorem 2al2imi 39272
Description: Removes two universal quantifiers from a statement. (Contributed by Andrew Salmon, 24-May-2011.)
Hypothesis
Ref Expression
2al2imi.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
2al2imi (∀𝑥𝑦𝜑 → (∀𝑥𝑦𝜓 → ∀𝑥𝑦𝜒))

Proof of Theorem 2al2imi
StepHypRef Expression
1 2al2imi.1 . . 3 (𝜑 → (𝜓𝜒))
21al2imi 1910 . 2 (∀𝑦𝜑 → (∀𝑦𝜓 → ∀𝑦𝜒))
32al2imi 1910 1 (∀𝑥𝑦𝜑 → (∀𝑥𝑦𝜓 → ∀𝑥𝑦𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1650
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1890  ax-4 1904
This theorem is referenced by:  2alim  39276
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