Metamath Proof Explorer


Theorem simp22

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

Ref Expression
Assertion simp22 ( ( 𝜑 ∧ ( 𝜓𝜒𝜃 ) ∧ 𝜏 ) → 𝜒 )

Proof

Step Hyp Ref Expression
1 simp2 ( ( 𝜓𝜒𝜃 ) → 𝜒 )
2 1 3ad2ant2 ( ( 𝜑 ∧ ( 𝜓𝜒𝜃 ) ∧ 𝜏 ) → 𝜒 )