Theorem imp4a

Description: An importation inference. (Contributed by NM, 26-Apr-1994) (Proof shortened by Wolf Lammen, 19-Jul-2021)

	Ref	Expression
Hypothesis	imp4.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )
Assertion	imp4a	⊢ ( 𝜑 → ( 𝜓 → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) ) )

Proof

Step	Hyp	Ref	Expression
1		imp4.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )
2	1	imp4b	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) )
3	2	ex	⊢ ( 𝜑 → ( 𝜓 → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) ) )