Metamath Proof Explorer


Theorem cbvmo

Description: Rule used to change bound variables, using implicit substitution. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker cbvmow , cbvmovw when possible. (Contributed by NM, 9-Mar-1995) (Revised by Andrew Salmon, 8-Jun-2011) (Proof shortened by Wolf Lammen, 4-Jan-2023) (New usage is discouraged.)

Ref Expression
Hypotheses cbvmo.1 y φ
cbvmo.2 x ψ
cbvmo.3 x = y φ ψ
Assertion cbvmo * x φ * y ψ

Proof

Step Hyp Ref Expression
1 cbvmo.1 y φ
2 cbvmo.2 x ψ
3 cbvmo.3 x = y φ ψ
4 1 sb8mo * x φ * y y x φ
5 2 3 sbie y x φ ψ
6 5 mobii * y y x φ * y ψ
7 4 6 bitri * x φ * y ψ