Theorem impac 649

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 575	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜓)))
3	2	imp 444	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∧ 𝜓))

Syntax hints:   → wi 4   ∧ wa 383

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 196  df-an 385

This theorem is referenced by:  imdistanri  723  f1elima  6421  zfrep6  7027  repswswrd  13382  clwwlknprop  26300  sltval2  31053  bj-snsetex  32144