Theorem impr

Description: Import a wff into a right conjunct. (Contributed by Jeff Hankins, 30-Aug-2009)

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

Proof

Step	Hyp	Ref	Expression
1		impr.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) )
2	1	ex	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
3	2	imp32	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )