Theorem 3expia

Description: Exportation from triple conjunction. (Contributed by NM, 19-May-2007) (Proof shortened by Wolf Lammen, 22-Jun-2022)

	Ref	Expression
Hypothesis	3exp.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	3expia	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		3exp.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
2	1	3expb	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
3	2	expr	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) )