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Theorem pm11.63 37420
Description: Theorem *11.63 in [WhiteheadRussell] p. 166. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
pm11.63 (¬ ∃𝑥𝑦𝜑 → ∀𝑥𝑦(𝜑𝜓))

Proof of Theorem pm11.63
StepHypRef Expression
1 2nexaln 1746 . 2 (¬ ∃𝑥𝑦𝜑 ↔ ∀𝑥𝑦 ¬ 𝜑)
2 pm2.21 118 . . 3 𝜑 → (𝜑𝜓))
322alimi 1730 . 2 (∀𝑥𝑦 ¬ 𝜑 → ∀𝑥𝑦(𝜑𝜓))
41, 3sylbi 205 1 (¬ ∃𝑥𝑦𝜑 → ∀𝑥𝑦(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1472  wex 1694
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727
This theorem depends on definitions:  df-bi 195  df-ex 1695
This theorem is referenced by: (None)
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