Theorem alsyl 1649

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		pm3.33 345	. 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜓 → 𝜒)) → (𝜑 → 𝜒))
2	1	alanimi 1473	1 ⊢ ((∀𝑥(𝜑 → 𝜓) ∧ ∀𝑥(𝜓 → 𝜒)) → ∀𝑥(𝜑 → 𝜒))

Syntax hints:   → wi 4   ∧ wa 104  ∀wal 1362

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1461  ax-gen 1463

This theorem is referenced by:  barbara  2143