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Theorem pm10.56 37415
Description: Theorem *10.56 in [WhiteheadRussell] p. 156. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
pm10.56 ((∀𝑥(𝜑𝜓) ∧ ∃𝑥(𝜑𝜒)) → ∃𝑥(𝜓𝜒))

Proof of Theorem pm10.56
StepHypRef Expression
1 pm3.45 874 . . 3 ((𝜑𝜓) → ((𝜑𝜒) → (𝜓𝜒)))
21aleximi 1748 . 2 (∀𝑥(𝜑𝜓) → (∃𝑥(𝜑𝜒) → ∃𝑥(𝜓𝜒)))
32imp 443 1 ((∀𝑥(𝜑𝜓) ∧ ∃𝑥(𝜑𝜒)) → ∃𝑥(𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  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-an 384  df-ex 1695
This theorem is referenced by: (None)
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