Theorem exp4b

Description: An exportation inference. (Contributed by NM, 26-Apr-1994) (Proof shortened by Wolf Lammen, 23-Nov-2012) Shorten exp4a . (Revised by Wolf Lammen, 20-Jul-2021)

	Ref	Expression
Hypothesis	exp4b.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) )
Assertion	exp4b	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		exp4b.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) )
2	1	expd	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
3	2	ex	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )