Theorem eel0000

Description: Elimination rule similar to mp4an , except with a left-nested conjunction unification theorem. (Contributed by Alan Sare, 17-Oct-2017)

	Ref	Expression
Hypotheses	eel0000.1	⊢ 𝜑
	eel0000.2	⊢ 𝜓
	eel0000.3	⊢ 𝜒
	eel0000.4	⊢ 𝜃
	eel0000.5	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )
Assertion	eel0000	⊢ 𝜏

Proof

Step	Hyp	Ref	Expression
1		eel0000.1	⊢ 𝜑
2		eel0000.2	⊢ 𝜓
3		eel0000.3	⊢ 𝜒
4		eel0000.4	⊢ 𝜃
5		eel0000.5	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )
6	5	exp41	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )
7	1 2 6	mp2	⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
8	3 4 7	mp2	⊢ 𝜏