Metamath Proof Explorer


Theorem coi1ss

Description: Precomposing with the identity yields a subclass. (Contributed by BJ, 8-Nov-2026) Can shorten mvdco .

Ref Expression
Assertion coi1ss ⊢ A ∘ I ⊆ A

Proof

Step Hyp Ref Expression
1 coi1res ⊢ A ∘ I = A ↾ V
2 resss ⊢ A ↾ V ⊆ A
3 1 2 eqsstri ⊢ A ∘ I ⊆ A