Metamath Proof Explorer

Theorem bnj252

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

Ref Expression
Assertion bnj252 ⊢ φ ∧ ψ ∧ χ ∧ θ ↔ φ ∧ ψ ∧ χ ∧ θ

Proof

Step Hyp Ref Expression
1 bnj250 ⊢ φ ∧ ψ ∧ χ ∧ θ ↔ φ ∧ ψ ∧ χ ∧ θ
2 df-3an ⊢ ψ ∧ χ ∧ θ ↔ ψ ∧ χ ∧ θ
3 2 anbi2i ⊢ φ ∧ ψ ∧ χ ∧ θ ↔ φ ∧ ψ ∧ χ ∧ θ
4 1 3 bitr4i ⊢ φ ∧ ψ ∧ χ ∧ θ ↔ φ ∧ ψ ∧ χ ∧ θ