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Theorem alsyl 1567
Description: 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 pm3.33 337 . 2 (((𝜑𝜓) ∧ (𝜓𝜒)) → (𝜑𝜒))
21alanimi 1389 1 ((∀𝑥(𝜑𝜓) ∧ ∀𝑥(𝜓𝜒)) → ∀𝑥(𝜑𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wal 1283
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379
This theorem is referenced by:  barbara  2040
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