Theorem bnj432 30035

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 30034	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜒 ∧ 𝜃 ∧ 𝜑 ∧ 𝜓))
2		bnj256 30025	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜑 ∧ 𝜓) ↔ ((𝜒 ∧ 𝜃) ∧ (𝜑 ∧ 𝜓)))
3	1, 2	bitri 263	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜒 ∧ 𝜃) ∧ (𝜑 ∧ 𝜓)))

Syntax hints:   ↔ wb 195   ∧ wa 383   ∧ w-bnj17 30005

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 196  df-an 385  df-3an 1033  df-bnj17 30006

This theorem is referenced by:  bnj605  30231  bnj600  30243