This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Rearrangement of 4 conjuncts. (Contributed by Rodolfo Medina, 24-Sep-2010) (Proof shortened by Andrew Salmon, 29-Jun-2011)
|
|
Ref |
Expression |
|
Assertion |
an43 |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜑 ∧ 𝜃 ) ∧ ( 𝜓 ∧ 𝜒 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
an42 |
⊢ ( ( ( 𝜑 ∧ 𝜃 ) ∧ ( 𝜓 ∧ 𝜒 ) ) ↔ ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ) |
| 2 |
1
|
bicomi |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜑 ∧ 𝜃 ) ∧ ( 𝜓 ∧ 𝜒 ) ) ) |