Theorem 3anrev 945

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

Assertion

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

Proof of Theorem 3anrev

Step	Hyp	Ref	Expression
1		3ancoma 941	. 2 ⊢ ((φ ∧ ψ ∧ χ) ↔ (ψ ∧ φ ∧ χ))
2		3anrot 939	. 2 ⊢ ((χ ∧ ψ ∧ φ) ↔ (ψ ∧ φ ∧ χ))
3	1, 2	bitr4i 243	1 ⊢ ((φ ∧ ψ ∧ χ) ↔ (χ ∧ ψ ∧ φ))

Syntax hints:   ↔ wb 176   ∧ 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:  3com13  1156