Metamath Proof Explorer


Theorem impac

Description: Importation with conjunction in consequent. (Contributed by NM, 9-Aug-1994)

Ref Expression
Hypothesis impac.1 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion impac ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 ∧ 𝜓 ) )

Proof

Step Hyp Ref Expression
1 impac.1 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2 1 ancrd ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 ∧ 𝜓 ) ) )
3 2 imp ⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 ∧ 𝜓 ) )