Metamath Proof Explorer
Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)
(Proof shortened by Andrew Salmon, 14-Jun-2011)
(New usage is discouraged.)
|
|
Ref |
Expression |
|
Assertion |
bnj170 |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜑 ) ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
3anrot |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜓 ∧ 𝜒 ∧ 𝜑 ) ) |
2 |
|
df-3an |
⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜑 ) ↔ ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜑 ) ) |
3 |
1 2
|
bitri |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜑 ) ) |