Theorem bnj334 34706

Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (New usage is discouraged.)

Assertion

Ref	Expression
bnj334	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜒 ∧ 𝜑 ∧ 𝜓 ∧ 𝜃))

Proof of Theorem bnj334

Step	Hyp	Ref	Expression
1		bnj290 34703	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓))
2		bnj257 34700	. 2 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓) ↔ (𝜑 ∧ 𝜒 ∧ 𝜓 ∧ 𝜃))
3		bnj312 34705	. 2 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜓 ∧ 𝜃) ↔ (𝜒 ∧ 𝜑 ∧ 𝜓 ∧ 𝜃))
4	1, 2, 3	3bitri 297	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜒 ∧ 𝜑 ∧ 𝜓 ∧ 𝜃))

Syntax hints:   ↔ wb 206   ∧ w-bnj17 34679

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 207  df-an 396  df-3an 1088  df-bnj17 34680

This theorem is referenced by:  bnj345  34707  bnj518  34879  bnj916  34926  bnj929  34929