Metamath Proof Explorer


Theorem cbvralsvw

Description: Change bound variable by using a substitution. Version of cbvralsv with a disjoint variable condition, which does not require ax-13 . (Contributed by NM, 20-Nov-2005) Avoid ax-13 . (Revised by Gino Giotto, 10-Jan-2024) (Proof shortened by Wolf Lammen, 8-Mar-2025)

Ref Expression
Assertion cbvralsvw x A φ y A y x φ

Proof

Step Hyp Ref Expression
1 nfv y φ
2 nfs1v x y x φ
3 sbequ12 x = y φ y x φ
4 1 2 3 cbvralw x A φ y A y x φ