Theorem pm3.31 432

Description: Theorem *3.31 (Imp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)

Assertion

Ref	Expression
pm3.31	⊢ ((φ → (ψ → χ)) → ((φ ∧ ψ) → χ))

Proof of Theorem pm3.31

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((φ → (ψ → χ)) → (φ → (ψ → χ)))
2	1	imp3a 420	1 ⊢ ((φ → (ψ → χ)) → ((φ ∧ ψ) → χ))

This proof depends on syntax axioms:   → wi 4   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is used by:  impexp  433  imp5a  581