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Theorem pm10.53 38391
Description: Theorem *10.53 in [WhiteheadRussell] p. 155. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
pm10.53 (¬ ∃𝑥𝜑 → ∀𝑥(𝜑𝜓))

Proof of Theorem pm10.53
StepHypRef Expression
1 pm2.21 120 . 2 (¬ ∃𝑥𝜑 → (∃𝑥𝜑 → ∀𝑥𝜓))
2 19.38 1765 . 2 ((∃𝑥𝜑 → ∀𝑥𝜓) → ∀𝑥(𝜑𝜓))
31, 2syl 17 1 (¬ ∃𝑥𝜑 → ∀𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1480  wex 1703
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1721  ax-4 1736
This theorem depends on definitions:  df-bi 197  df-ex 1704
This theorem is referenced by: (None)
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