Theorem bnj255 34903

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

Assertion

Ref	Expression
bnj255	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃)))

Proof of Theorem bnj255

Step	Hyp	Ref	Expression
1		bnj251 34900	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃))))
2		3anass 1101	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃)) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃))))
3	1, 2	bitr4i 280	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃)))

Syntax hints:   ↔ wb 208   ∧ wa 397   ∧ 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:  bnj964  35140  bnj998  35154  bnj1033  35166  bnj1175  35201