Metamath Proof Explorer


Theorem bnj291

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Assertion bnj291 ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( ( 𝜑 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜓 ) )

Proof

Step Hyp Ref Expression
1 bnj290 ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓 ) )
2 df-bnj17 ⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓 ) ↔ ( ( 𝜑 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜓 ) )
3 1 2 bitri ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( ( 𝜑 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜓 ) )