Theorem an31 775

Description: A rearrangement of conjuncts. (Contributed by NM, 24-Jun-2012.) (Proof shortened by Wolf Lammen, 31-Dec-2012.)

Assertion

Ref	Expression
an31	⊢ (((φ ∧ ψ) ∧ χ) ↔ ((χ ∧ ψ) ∧ φ))

Proof of Theorem an31

Step	Hyp	Ref	Expression
1		an13 774	. 2 ⊢ ((φ ∧ (ψ ∧ χ)) ↔ (χ ∧ (ψ ∧ φ)))
2		anass 630	. 2 ⊢ (((φ ∧ ψ) ∧ χ) ↔ (φ ∧ (ψ ∧ χ)))
3		anass 630	. 2 ⊢ (((χ ∧ ψ) ∧ φ) ↔ (χ ∧ (ψ ∧ φ)))
4	1, 2, 3	3bitr4i 268	1 ⊢ (((φ ∧ ψ) ∧ χ) ↔ ((χ ∧ ψ) ∧ φ))

This proof depends on syntax axioms:   ↔ wb 176   ∧ wa 358

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

This theorem is used by:  euind  3024  reuind  3040