Theorem bnj256 32086

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

Assertion

Ref	Expression
bnj256	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)))

Proof of Theorem bnj256

Step	Hyp	Ref	Expression
1		bnj248 32080	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃))
2		anass 472	. 2 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)))
3	1, 2	bitri 278	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)))

Syntax hints:   ↔ wb 209   ∧ wa 399   ∧ w-bnj17 32066

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 210  df-an 400  df-3an 1086  df-bnj17 32067

This theorem is referenced by:  bnj257  32087  bnj432  32096  bnj543  32275  bnj546  32278  bnj557  32283  bnj916  32315  bnj969  32328  bnj1090  32361  bnj1118  32366  bnj1174  32385