Theorem bnj432 30782

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

Assertion

Ref	Expression
bnj432	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜒 ∧ 𝜃) ∧ (𝜑 ∧ 𝜓)))

Proof of Theorem bnj432

Step	Hyp	Ref	Expression
1		bnj422 30781	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜒 ∧ 𝜃 ∧ 𝜑 ∧ 𝜓))
2		bnj256 30772	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜑 ∧ 𝜓) ↔ ((𝜒 ∧ 𝜃) ∧ (𝜑 ∧ 𝜓)))
3	1, 2	bitri 264	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜒 ∧ 𝜃) ∧ (𝜑 ∧ 𝜓)))

Syntax hints:   ↔ wb 196   ∧ wa 384   ∧ 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:  bnj605  30977  bnj600  30989