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Metamath Proof Explorer

Theorem resabs1d

Description: Absorption law for restriction, deduction form. (Contributed by Glauco Siliprandi, 11-Dec-2019)

Ref Expression
Hypothesis resabs1d.b ⊢ φ → B ⊆ C
Assertion resabs1d ⊢ φ → A ↾ C ↾ B = A ↾ B

Proof

Step Hyp Ref Expression
1 resabs1d.b ⊢ φ → B ⊆ C
2 resabs1 ⊢ B ⊆ C → A ↾ C ↾ B = A ↾ B
3 1 2 syl ⊢ φ → A ↾ C ↾ B = A ↾ B