Theorem impac 378

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 324	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜓)))
3	2	imp 123	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∧ 𝜓))

Syntax hints:   → wi 4   ∧ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by:  imdistanri  442  f1elima  5674