Theorem impac 562

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 561	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜓)))
3	2	imp 412	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∧ 𝜓))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  imdistanri  580  f1elima  7267  zfrep6OLD  7967  repswswrd  14935  ltsval2  28013  bj-snsetex  37876