Description: Difference law for Cartesian products. (Contributed by Thierry Arnoux, 24-Jul-2023)
Ref | Expression | ||
---|---|---|---|
Assertion | difxp1ss | ⊢ ( ( 𝐴 ∖ 𝐶 ) × 𝐵 ) ⊆ ( 𝐴 × 𝐵 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | difxp1 | ⊢ ( ( 𝐴 ∖ 𝐶 ) × 𝐵 ) = ( ( 𝐴 × 𝐵 ) ∖ ( 𝐶 × 𝐵 ) ) | |
2 | difss | ⊢ ( ( 𝐴 × 𝐵 ) ∖ ( 𝐶 × 𝐵 ) ) ⊆ ( 𝐴 × 𝐵 ) | |
3 | 1 2 | eqsstri | ⊢ ( ( 𝐴 ∖ 𝐶 ) × 𝐵 ) ⊆ ( 𝐴 × 𝐵 ) |