Metamath Proof Explorer

Theorem simpl21

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012) (Proof shortened by Wolf Lammen, 24-Jun-2022)

Ref Expression
Assertion simpl21 ⊢ θ ∧ φ ∧ ψ ∧ χ ∧ τ ∧ η → φ

Proof

Step Hyp Ref Expression
1 simpl1 ⊢ φ ∧ ψ ∧ χ ∧ η → φ
2 1 3ad2antl2 ⊢ θ ∧ φ ∧ ψ ∧ χ ∧ τ ∧ η → φ