Theorem bnj170 35057

Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (New usage is discouraged.)

Assertion

Ref	Expression
bnj170	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ ((𝜓 ∧ 𝜒) ∧ 𝜑))

Proof of Theorem bnj170

Step	Hyp	Ref	Expression
1		3anrot 1115	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜓 ∧ 𝜒 ∧ 𝜑))
2		df-3an 1103	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) ↔ ((𝜓 ∧ 𝜒) ∧ 𝜑))
3	1, 2	bitri 278	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ ((𝜓 ∧ 𝜒) ∧ 𝜑))

Syntax hints:   ↔ wb 209   ∧ wa 400   ∧ w3a 1101

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 210  df-an 401  df-3an 1103

This theorem is referenced by:  bnj543  35251  bnj605  35265  bnj594  35270  bnj607  35274  bnj908  35289  bnj1173  35360