Theorem alsyl 1615

Description: Theorem *10.3 in [WhiteheadRussell] p. 150. (Contributed by Andrew Salmon, 8-Jun-2011.)

Assertion

Ref	Expression
alsyl	⊢ ((∀x(φ → ψ) ∧ ∀x(ψ → χ)) → ∀x(φ → χ))

Proof of Theorem alsyl

Step	Hyp	Ref	Expression
1		pm3.33 568	. 2 ⊢ (((φ → ψ) ∧ (ψ → χ)) → (φ → χ))
2	1	alanimi 1562	1 ⊢ ((∀x(φ → ψ) ∧ ∀x(ψ → χ)) → ∀x(φ → χ))

Syntax hints:   → wi 4   ∧ wa 358  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  barbara  2301