Metamath Proof Explorer

Theorem simp21

Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011)

Ref Expression
Assertion simp21 ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜏 ) → 𝜓 )

Proof

Step Hyp Ref Expression
1 simp1 ⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜓 )
2 1 3ad2ant2 ⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜏 ) → 𝜓 )