Description: Absorption law for restriction. (Contributed by NM, 27-Mar-1998)
Ref | Expression | ||
---|---|---|---|
Assertion | resabs2 | ⊢ ( 𝐵 ⊆ 𝐶 → ( ( 𝐴 ↾ 𝐵 ) ↾ 𝐶 ) = ( 𝐴 ↾ 𝐵 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rescom | ⊢ ( ( 𝐴 ↾ 𝐵 ) ↾ 𝐶 ) = ( ( 𝐴 ↾ 𝐶 ) ↾ 𝐵 ) | |
2 | resabs1 | ⊢ ( 𝐵 ⊆ 𝐶 → ( ( 𝐴 ↾ 𝐶 ) ↾ 𝐵 ) = ( 𝐴 ↾ 𝐵 ) ) | |
3 | 1 2 | eqtrid | ⊢ ( 𝐵 ⊆ 𝐶 → ( ( 𝐴 ↾ 𝐵 ) ↾ 𝐶 ) = ( 𝐴 ↾ 𝐵 ) ) |