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 ) ) ) |