Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | bnj290 | ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3anrot | ⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜒 ∧ 𝜃 ∧ 𝜓 ) ) | |
2 | 1 | anbi2i | ⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ) ↔ ( 𝜑 ∧ ( 𝜒 ∧ 𝜃 ∧ 𝜓 ) ) ) |
3 | bnj252 | ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ) ) | |
4 | bnj252 | ⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓 ) ↔ ( 𝜑 ∧ ( 𝜒 ∧ 𝜃 ∧ 𝜓 ) ) ) | |
5 | 2 3 4 | 3bitr4i | ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓 ) ) |