Metamath Proof Explorer

Theorem simp13

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

Ref Expression
Assertion simp13 ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ∧ 𝜏 ) → 𝜒 )

Proof

Step Hyp Ref Expression
1 simp3 ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜒 )
2 1 3ad2ant1 ⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ∧ 𝜏 ) → 𝜒 )