Theorem pm3.33 761

Description: Theorem *3.33 (Syll) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm3.33	⊢ (((𝜑 → 𝜓) ∧ (𝜓 → 𝜒)) → (𝜑 → 𝜒))

Proof of Theorem pm3.33

Step	Hyp	Ref	Expression
1		imim1 83	. 2 ⊢ ((𝜑 → 𝜓) → ((𝜓 → 𝜒) → (𝜑 → 𝜒)))
2	1	imp 406	1 ⊢ (((𝜑 → 𝜓) ∧ (𝜓 → 𝜒)) → (𝜑 → 𝜒))

Syntax hints:   → wi 4   ∧ wa 395

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

This theorem depends on definitions:  df-bi 206  df-an 396

This theorem is referenced by:  alsyl  1897  ucncn  23345  bnj1023  32660  bnj907  32847  2sb5ndALT  42441