Description: Rearrangement of 4 conjuncts. (Contributed by NM, 7-Feb-1996)
Ref | Expression | ||
---|---|---|---|
Assertion | an42 | ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜑 ∧ 𝜒 ) ∧ ( 𝜃 ∧ 𝜓 ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | an4 | ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜑 ∧ 𝜒 ) ∧ ( 𝜓 ∧ 𝜃 ) ) ) | |
2 | ancom | ⊢ ( ( 𝜓 ∧ 𝜃 ) ↔ ( 𝜃 ∧ 𝜓 ) ) | |
3 | 2 | anbi2i | ⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ ( 𝜓 ∧ 𝜃 ) ) ↔ ( ( 𝜑 ∧ 𝜒 ) ∧ ( 𝜃 ∧ 𝜓 ) ) ) |
4 | 1 3 | bitri | ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜑 ∧ 𝜒 ) ∧ ( 𝜃 ∧ 𝜓 ) ) ) |