Theorem eel0000 42293

Description: Elimination rule similar to mp4an 689, except with a left-nested conjunction unification theorem. (Contributed by Alan Sare, 17-Oct-2017.)

Hypotheses

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

Assertion

Ref	Expression
eel0000	⊢ 𝜏

Proof of Theorem eel0000

Step	Hyp	Ref	Expression
1		eel0000.3	. 2 ⊢ 𝜒
2		eel0000.4	. 2 ⊢ 𝜃
3		eel0000.1	. . 3 ⊢ 𝜑
4		eel0000.2	. . 3 ⊢ 𝜓
5		eel0000.5	. . . 4 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)
6	5	exp41 434	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))
7	3, 4, 6	mp2 9	. 2 ⊢ (𝜒 → (𝜃 → 𝜏))
8	1, 2, 7	mp2 9	1 ⊢ 𝜏

Syntax hints:   → wi 4   ∧ wa 395

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 396

This theorem is referenced by: (None)