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Theorem 2albi 38056
Description: Theorem *11.33 in [WhiteheadRussell] p. 162. Theorem 19.15 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
2albi (∀𝑥𝑦(𝜑𝜓) → (∀𝑥𝑦𝜑 ↔ ∀𝑥𝑦𝜓))

Proof of Theorem 2albi
StepHypRef Expression
1 albi 1743 . . 3 (∀𝑦(𝜑𝜓) → (∀𝑦𝜑 ↔ ∀𝑦𝜓))
21alimi 1736 . 2 (∀𝑥𝑦(𝜑𝜓) → ∀𝑥(∀𝑦𝜑 ↔ ∀𝑦𝜓))
3 albi 1743 . 2 (∀𝑥(∀𝑦𝜑 ↔ ∀𝑦𝜓) → (∀𝑥𝑦𝜑 ↔ ∀𝑥𝑦𝜓))
42, 3syl 17 1 (∀𝑥𝑦(𝜑𝜓) → (∀𝑥𝑦𝜑 ↔ ∀𝑥𝑦𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734
This theorem depends on definitions:  df-bi 197
This theorem is referenced by: (None)
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