Theorem 3anrot 939

Description: Rotation law for triple conjunction. (Contributed by NM, 8-Apr-1994.)

Assertion

Ref	Expression
3anrot	⊢ ((φ ∧ ψ ∧ χ) ↔ (ψ ∧ χ ∧ φ))

Proof of Theorem 3anrot

Step	Hyp	Ref	Expression
1		ancom 437	. 2 ⊢ ((φ ∧ (ψ ∧ χ)) ↔ ((ψ ∧ χ) ∧ φ))
2		3anass 938	. 2 ⊢ ((φ ∧ ψ ∧ χ) ↔ (φ ∧ (ψ ∧ χ)))
3		df-3an 936	. 2 ⊢ ((ψ ∧ χ ∧ φ) ↔ ((ψ ∧ χ) ∧ φ))
4	1, 2, 3	3bitr4i 268	1 ⊢ ((φ ∧ ψ ∧ χ) ↔ (ψ ∧ χ ∧ φ))

Syntax hints:   ↔ wb 176   ∧ wa 358   ∧ w3a 934

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 177  df-an 360  df-3an 936

This theorem is referenced by:  3ancomb  943  3anrev  945  3simpc  954  oqelins4  5795  leaddc2  6216  lemuc2  6255