Metamath Proof Explorer


Theorem bnj770

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

Ref Expression
Hypotheses bnj770.1 ⊢ η ↔ φ ∧ ψ ∧ χ ∧ θ
bnj770.2 ⊢ ψ → τ
Assertion bnj770 ⊢ η → τ

Proof

Step Hyp Ref Expression
1 bnj770.1 ⊢ η ↔ φ ∧ ψ ∧ χ ∧ θ
2 bnj770.2 ⊢ ψ → τ
3 2 bnj706 ⊢ φ ∧ ψ ∧ χ ∧ θ → τ
4 1 3 sylbi ⊢ η → τ