Theorem 3ancomb 943

Description: Commutation law for triple conjunction. (Contributed by NM, 21-Apr-1994.)

Assertion

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

Proof of Theorem 3ancomb

Step	Hyp	Ref	Expression
1		3ancoma 941	. 2 ⊢ ((φ ∧ ψ ∧ χ) ↔ (ψ ∧ φ ∧ χ))
2		3anrot 939	. 2 ⊢ ((ψ ∧ φ ∧ χ) ↔ (φ ∧ χ ∧ ψ))
3	1, 2	bitri 240	1 ⊢ ((φ ∧ ψ ∧ χ) ↔ (φ ∧ χ ∧ ψ))

This proof depends on syntax axioms:   ↔ wb 176   ∧ w3a 934

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is used by:  3simpb  953