Description: Rearrangement of 4 disjuncts. (Contributed by NM, 10-Jan-2005)
Ref | Expression | ||
---|---|---|---|
Assertion | or42 | ⊢ ( ( ( 𝜑 ∨ 𝜓 ) ∨ ( 𝜒 ∨ 𝜃 ) ) ↔ ( ( 𝜑 ∨ 𝜒 ) ∨ ( 𝜃 ∨ 𝜓 ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | or4 | ⊢ ( ( ( 𝜑 ∨ 𝜓 ) ∨ ( 𝜒 ∨ 𝜃 ) ) ↔ ( ( 𝜑 ∨ 𝜒 ) ∨ ( 𝜓 ∨ 𝜃 ) ) ) | |
2 | orcom | ⊢ ( ( 𝜓 ∨ 𝜃 ) ↔ ( 𝜃 ∨ 𝜓 ) ) | |
3 | 2 | orbi2i | ⊢ ( ( ( 𝜑 ∨ 𝜒 ) ∨ ( 𝜓 ∨ 𝜃 ) ) ↔ ( ( 𝜑 ∨ 𝜒 ) ∨ ( 𝜃 ∨ 𝜓 ) ) ) |
4 | 1 3 | bitri | ⊢ ( ( ( 𝜑 ∨ 𝜓 ) ∨ ( 𝜒 ∨ 𝜃 ) ) ↔ ( ( 𝜑 ∨ 𝜒 ) ∨ ( 𝜃 ∨ 𝜓 ) ) ) |