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 ( ( ( ( 𝜑𝜓 ) ∧ 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 ( ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )
6 5 exp41 ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) ) )
7 1 2 6 mp2 ( 𝜒 → ( 𝜃𝜏 ) )
8 3 4 7 mp2 𝜏