Metamath Proof Explorer


Theorem itgeq2sdv

Description: Equality theorem for an integral. Deduction form. (Contributed by GG, 1-Sep-2025)

Ref Expression
Hypothesis itgeq2sdv.1 ⊢ φ → B = C
Assertion itgeq2sdv ⊢ φ → ∫ A B dx = ∫ A C dx

Proof

Step Hyp Ref Expression
1 itgeq2sdv.1 ⊢ φ → B = C
2 eqidd ⊢ φ → A = A
3 2 1 itgeq12sdv ⊢ φ → ∫ A B dx = ∫ A C dx