Theorem bnj255 30771

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 30768	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃))))
2		3anass 1042	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃)) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃))))
3	1, 2	bitr4i 267	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃)))

Syntax hints:   ↔ wb 196   ∧ wa 384   ∧ w3a 1037   ∧ w-bnj17 30752

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 197  df-an 386  df-3an 1039  df-bnj17 30753

This theorem is referenced by:  bnj964  31013  bnj998  31026  bnj1033  31037  bnj1175  31072