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Theorem pm11.12 37395
Description: Theorem *11.12 in [WhiteheadRussell] p. 159. (Contributed by Andrew Salmon, 17-Jun-2011.)
Assertion
Ref Expression
pm11.12 (∀𝑥𝑦(𝜑𝜓) → (𝜑 ∨ ∀𝑥𝑦𝜓))
Distinct variable groups:   𝜑,𝑥   𝜑,𝑦
Allowed substitution hints:   𝜓(𝑥,𝑦)

Proof of Theorem pm11.12
StepHypRef Expression
1 pm10.12 37378 . . 3 (∀𝑦(𝜑𝜓) → (𝜑 ∨ ∀𝑦𝜓))
21alimi 1728 . 2 (∀𝑥𝑦(𝜑𝜓) → ∀𝑥(𝜑 ∨ ∀𝑦𝜓))
3 pm10.12 37378 . 2 (∀𝑥(𝜑 ∨ ∀𝑦𝜓) → (𝜑 ∨ ∀𝑥𝑦𝜓))
42, 3syl 17 1 (∀𝑥𝑦(𝜑𝜓) → (𝜑 ∨ ∀𝑥𝑦𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 381  wal 1472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825
This theorem depends on definitions:  df-bi 195  df-or 383  df-ex 1695
This theorem is referenced by: (None)
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