Theorem bnj290 35043

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

Assertion

Ref	Expression
bnj290	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓))

Proof of Theorem bnj290

Step	Hyp	Ref	Expression
1		3anrot 1115	. . 3 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜒 ∧ 𝜃 ∧ 𝜓))
2	1	anbi2i 634	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) ↔ (𝜑 ∧ (𝜒 ∧ 𝜃 ∧ 𝜓)))
3		bnj252 35036	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)))
4		bnj252 35036	. 2 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓) ↔ (𝜑 ∧ (𝜒 ∧ 𝜃 ∧ 𝜓)))
5	2, 3, 4	3bitr4i 306	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓))

Syntax hints:   ↔ wb 209   ∧ wa 400   ∧ w3a 1101   ∧ w-bnj17 35019

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 401  df-3an 1103  df-bnj17 35020

This theorem is referenced by:  bnj291  35044  bnj334  35046