Description: Rearrangement of 4 disjuncts. (Contributed by NM, 12-Aug-1994)
Ref | Expression | ||
---|---|---|---|
Assertion | or4 | ⊢ ( ( ( 𝜑 ∨ 𝜓 ) ∨ ( 𝜒 ∨ 𝜃 ) ) ↔ ( ( 𝜑 ∨ 𝜒 ) ∨ ( 𝜓 ∨ 𝜃 ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | or12 | ⊢ ( ( 𝜓 ∨ ( 𝜒 ∨ 𝜃 ) ) ↔ ( 𝜒 ∨ ( 𝜓 ∨ 𝜃 ) ) ) | |
2 | 1 | orbi2i | ⊢ ( ( 𝜑 ∨ ( 𝜓 ∨ ( 𝜒 ∨ 𝜃 ) ) ) ↔ ( 𝜑 ∨ ( 𝜒 ∨ ( 𝜓 ∨ 𝜃 ) ) ) ) |
3 | orass | ⊢ ( ( ( 𝜑 ∨ 𝜓 ) ∨ ( 𝜒 ∨ 𝜃 ) ) ↔ ( 𝜑 ∨ ( 𝜓 ∨ ( 𝜒 ∨ 𝜃 ) ) ) ) | |
4 | orass | ⊢ ( ( ( 𝜑 ∨ 𝜒 ) ∨ ( 𝜓 ∨ 𝜃 ) ) ↔ ( 𝜑 ∨ ( 𝜒 ∨ ( 𝜓 ∨ 𝜃 ) ) ) ) | |
5 | 2 3 4 | 3bitr4i | ⊢ ( ( ( 𝜑 ∨ 𝜓 ) ∨ ( 𝜒 ∨ 𝜃 ) ) ↔ ( ( 𝜑 ∨ 𝜒 ) ∨ ( 𝜓 ∨ 𝜃 ) ) ) |