Theorem 3anan12 947

Description: Convert triple conjunction to conjunction, then commute. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)

Assertion

Ref	Expression
3anan12	⊢ ((φ ∧ ψ ∧ χ) ↔ (ψ ∧ (φ ∧ χ)))

Proof of Theorem 3anan12

Step	Hyp	Ref	Expression
1		3ancoma 941	. 2 ⊢ ((φ ∧ ψ ∧ χ) ↔ (ψ ∧ φ ∧ χ))
2		3anass 938	. 2 ⊢ ((ψ ∧ φ ∧ χ) ↔ (ψ ∧ (φ ∧ χ)))
3	1, 2	bitri 240	1 ⊢ ((φ ∧ ψ ∧ χ) ↔ (ψ ∧ (φ ∧ χ)))

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:  2reu5lem3  3044