Theorem pm3.34 569

Description: Theorem *3.34 (Syll) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm3.34	⊢ (((ψ → χ) ∧ (φ → ψ)) → (φ → χ))

Proof of Theorem pm3.34

Step	Hyp	Ref	Expression
1		imim2 49	. 2 ⊢ ((ψ → χ) → ((φ → ψ) → (φ → χ)))
2	1	imp 418	1 ⊢ (((ψ → χ) ∧ (φ → ψ)) → (φ → χ))

Syntax hints:   → wi 4   ∧ wa 358

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 177  df-an 360

This theorem is referenced by: (None)