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Theorem alsyl 1894
Description: Universally quantified and uncurried (imported) form of syllogism. Theorem *10.3 in [WhiteheadRussell] p. 150. (Contributed by Andrew Salmon, 8-Jun-2011.)
Assertion
Ref Expression
alsyl ((∀𝑥(𝜑𝜓) ∧ ∀𝑥(𝜓𝜒)) → ∀𝑥(𝜑𝜒))

Proof of Theorem alsyl
StepHypRef Expression
1 pm3.33 763 . 2 (((𝜑𝜓) ∧ (𝜓𝜒)) → (𝜑𝜒))
21alanimi 1817 1 ((∀𝑥(𝜑𝜓) ∧ ∀𝑥(𝜓𝜒)) → ∀𝑥(𝜑𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  wal 1535
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810
This theorem depends on definitions:  df-bi 209  df-an 399
This theorem is referenced by:  eu6lem  2657  barbara  2747
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