Theorem pm3.3 431

Description: Theorem *3.3 (Exp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)

Assertion

Ref	Expression
pm3.3	⊢ (((φ ∧ ψ) → χ) → (φ → (ψ → χ)))

Proof of Theorem pm3.3

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (((φ ∧ ψ) → χ) → ((φ ∧ ψ) → χ))
2	1	exp3a 425	1 ⊢ (((φ ∧ ψ) → χ) → (φ → (ψ → 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:  impexp  433  pm4.79  566