Theorem bnj667 34950

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

Assertion

Ref	Expression
bnj667	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → (𝜓 ∧ 𝜒 ∧ 𝜃))

Proof of Theorem bnj667

Step	Hyp	Ref	Expression
1		bnj446 34915	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜑))
2	1	simplbi 498	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → (𝜓 ∧ 𝜒 ∧ 𝜃))

Syntax hints:   → wi 4   ∧ w3a 1093   ∧ w-bnj17 34884

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 209  df-an 398  df-3an 1095  df-bnj17 34885

This theorem is referenced by:  bnj570  35102  bnj594  35109  bnj944  35135  bnj969  35143