Description: Two ways of saying that two classes are disjoint (when C = (/) : ( ( A i^i B ) = (/) <-> ( B i^i A ) = (/) ) ). (Contributed by Peter Mazsa, 22-Mar-2017)
Ref | Expression | ||
---|---|---|---|
Assertion | ineqcom | ⊢ ( ( 𝐴 ∩ 𝐵 ) = 𝐶 ↔ ( 𝐵 ∩ 𝐴 ) = 𝐶 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | incom | ⊢ ( 𝐴 ∩ 𝐵 ) = ( 𝐵 ∩ 𝐴 ) | |
2 | 1 | eqeq1i | ⊢ ( ( 𝐴 ∩ 𝐵 ) = 𝐶 ↔ ( 𝐵 ∩ 𝐴 ) = 𝐶 ) |