Step |
Hyp |
Ref |
Expression |
1 |
|
bnj334 |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜒 ∧ 𝜑 ∧ 𝜓 ∧ 𝜃 ) ) |
2 |
|
bnj250 |
⊢ ( ( 𝜒 ∧ 𝜑 ∧ 𝜓 ∧ 𝜃 ) ↔ ( 𝜒 ∧ ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜃 ) ) ) |
3 |
|
3anass |
⊢ ( ( 𝜒 ∧ ( 𝜑 ∧ 𝜓 ) ∧ 𝜃 ) ↔ ( 𝜒 ∧ ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜃 ) ) ) |
4 |
2 3
|
bitr4i |
⊢ ( ( 𝜒 ∧ 𝜑 ∧ 𝜓 ∧ 𝜃 ) ↔ ( 𝜒 ∧ ( 𝜑 ∧ 𝜓 ) ∧ 𝜃 ) ) |
5 |
|
3anrev |
⊢ ( ( 𝜒 ∧ ( 𝜑 ∧ 𝜓 ) ∧ 𝜃 ) ↔ ( 𝜃 ∧ ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ) |
6 |
|
bnj250 |
⊢ ( ( 𝜃 ∧ 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜃 ∧ ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ) ) |
7 |
|
3anass |
⊢ ( ( 𝜃 ∧ ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ↔ ( 𝜃 ∧ ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ) ) |
8 |
6 7
|
bitr4i |
⊢ ( ( 𝜃 ∧ 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜃 ∧ ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ) |
9 |
5 8
|
bitr4i |
⊢ ( ( 𝜒 ∧ ( 𝜑 ∧ 𝜓 ) ∧ 𝜃 ) ↔ ( 𝜃 ∧ 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) |
10 |
1 4 9
|
3bitri |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜃 ∧ 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) |