Metamath Proof Explorer


Theorem coeq1i

Description: Equality inference for composition of two classes. (Contributed by NM, 16-Nov-2000)

Ref Expression
Hypothesis coeq1i.1 ⊢ A = B
Assertion coeq1i ⊢ A ∘ C = B ∘ C

Proof

Step Hyp Ref Expression
1 coeq1i.1 ⊢ A = B
2 coeq1 ⊢ A = B → A ∘ C = B ∘ C
3 1 2 ax-mp ⊢ A ∘ C = B ∘ C