Theorem 3anrot 586

Description: Rotation law for triple conjunction.

Assertion

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

Proof of Theorem 3anrot

Step	Hyp	Ref	Expression
1		ancom 333	. 2 ⊢ ((φ ∧ (ψ ∧ χ)) ↔ ((ψ ∧ χ) ∧ φ))
2		3anass 585	. 2 ⊢ ((φ ∧ ψ ∧ χ) ↔ (φ ∧ (ψ ∧ χ)))
3		df-3an 583	. 2 ⊢ ((ψ ∧ χ ∧ φ) ↔ ((ψ ∧ χ) ∧ φ))
4	1, 2, 3	3bitr4 158	1 ⊢ ((φ ∧ ψ ∧ χ) ↔ (ψ ∧ χ ∧ φ))

Syntax hints:   ↔ wb 127   ∧ wa 196   ∧ w3a 581

This theorem is referenced by:  3ancomb 589  3anrev 590  3simpc 593  fr3nr 2178  wefrc 2195  ordelord 2221  nnleltp1t 4448

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198  df-3an 583

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