Metamath Proof Explorer

Theorem bnj250

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

Ref Expression
Assertion bnj250 ⊢ φ ∧ ψ ∧ χ ∧ θ ↔ φ ∧ ψ ∧ χ ∧ θ

Proof

Step Hyp Ref Expression
1 df-bnj17 ⊢ φ ∧ ψ ∧ χ ∧ θ ↔ φ ∧ ψ ∧ χ ∧ θ
2 3anass ⊢ φ ∧ ψ ∧ χ ↔ φ ∧ ψ ∧ χ
3 2 anbi1i ⊢ φ ∧ ψ ∧ χ ∧ θ ↔ φ ∧ ψ ∧ χ ∧ θ
4 anass ⊢ φ ∧ ψ ∧ χ ∧ θ ↔ φ ∧ ψ ∧ χ ∧ θ
5 1 3 4 3bitri ⊢ φ ∧ ψ ∧ χ ∧ θ ↔ φ ∧ ψ ∧ χ ∧ θ