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Theorem pm10.12 37476
Description: Theorem *10.12 in [WhiteheadRussell] p. 146. In *10, this is treated as an axiom, and the proofs in *10 are based on this theorem. (Contributed by Andrew Salmon, 17-Jun-2011.)
Assertion
Ref Expression
pm10.12 (∀𝑥(𝜑𝜓) → (𝜑 ∨ ∀𝑥𝜓))
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem pm10.12
StepHypRef Expression
1 19.32v 1822 . 2 (∀𝑥(𝜑𝜓) ↔ (𝜑 ∨ ∀𝑥𝜓))
21biimpi 204 1 (∀𝑥(𝜑𝜓) → (𝜑 ∨ ∀𝑥𝜓))
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 1700  ax-4 1713  ax-5 1793
This theorem depends on definitions:  df-bi 195  df-or 383  df-ex 1695
This theorem is referenced by:  pm11.12  37493
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