Theorem bnj658 34724

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

Assertion

Ref	Expression
bnj658	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → (𝜑 ∧ 𝜓 ∧ 𝜒))

Proof of Theorem bnj658

Step	Hyp	Ref	Expression
1		df-bnj17 34660	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃))
2	1	simplbi 497	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → (𝜑 ∧ 𝜓 ∧ 𝜒))

Syntax hints:   → wi 4   ∧ w3a 1086   ∧ w-bnj17 34659

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-bnj17 34660

This theorem is referenced by:  bnj721  34730  bnj594  34885  bnj944  34911  bnj966  34917  bnj967  34918  bnj1154  34972