Theorem impac 381

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 326	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜓)))
3	2	imp 124	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∧ 𝜓))

This proof depends on syntax axioms:   → wi 4   ∧ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is used by:  imdistanri  450  f1elima  5979