Theorem impac 604

Description: Importation with conjunction in consequent. (Contributed by NM, 9-Aug-1994.)

Hypothesis

Ref	Expression
impac.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
impac	⊢ ((φ ∧ ψ) → (χ ∧ ψ))

Proof of Theorem impac

Step	Hyp	Ref	Expression
1		impac.1	. . 3 ⊢ (φ → (ψ → χ))
2	1	ancrd 537	. 2 ⊢ (φ → (ψ → (χ ∧ ψ)))
3	2	imp 418	1 ⊢ ((φ ∧ ψ) → (χ ∧ ψ))

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:  imdistanri  672  f1elima  5475