Theorem impac 552

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 551	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜓)))
3	2	imp 406	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∧ 𝜓))

Syntax hints:   → wi 4   ∧ wa 395

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 206  df-an 396

This theorem is referenced by:  imdistanri  569  f1elima  7117  zfrep6  7771  repswswrd  14425  sltval2  33786  bj-snsetex  35080