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Metamath Proof Explorer

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