Metamath Proof Explorer


Theorem bnj771

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

Ref Expression
Hypotheses bnj771.1 ⊢ η ↔ φ ∧ ψ ∧ χ ∧ θ
bnj771.2 ⊢ χ → τ
Assertion bnj771 ⊢ η → τ

Proof

Step Hyp Ref Expression
1 bnj771.1 ⊢ η ↔ φ ∧ ψ ∧ χ ∧ θ
2 bnj771.2 ⊢ χ → τ
3 2 bnj707 ⊢ φ ∧ ψ ∧ χ ∧ θ → τ
4 1 3 sylbi ⊢ η → τ